Basic limb kinematics of small therian mammals

1315 The Journal of Experimental Biology 205, 1315–1338 (2002) Printed in Great Britain © The Company of Biologists Limited 2002 JEB4010 Basic limb kinematics of small therian mammals Martin S. Fischer1,*, Nadja Schilling1, Manuela Schmidt1, Dieter Haarhaus2 and Hartmut Witte1 1Institut für Spezielle Zoologie und Evolutionsbiologie, Friedrich-Schiller-Universität, Jena, Erbertstrasse 1, D-07743 Jena, Germany and 2IWF Knowledge and Media gGmbH, Nonnenstieg 72, D-37075 Göttingen, PO box 2351, Germany *e-mail: [email protected] or [email protected] Accepted 12 February 2002 Summary A comparative study of quantitative kinematic data the limb. While kinematic parameters of forelimbs are of fore- and hindlimb movements of eight different independent of speed and gait (with the scapula as the mammalian species leads to the recognition of basic dominant element), fundamental changes occur in principles in the locomotion of small therians. The hindlimb kinematics with the change from symmetrical to description of kinematics comprises fore- and hindlimb in-phase gaits. Forward motion of the hindlimbs is now movements as well as sagittal spine movements including mainly due to sagittal lumbar spine movements displacement patterns of limb segments, their contribution contributing to half of the step length. Kinematics of small to step length, and joint movements. The comparison of therian mammals are independent of their systematic the contributions of different segments to step length position, their natural habitat, and also of specific clearly shows the proximal parts (scapula, femur) to anatomical dispositions (e.g. reduction of fingers, toes, or produce more than half of the propulsive movement of the clavicle). In contrast, the possession of a tail influences whole limb at symmetrical gaits. Basically, a three‘pelvic movements’. segmented limb with zigzag configuration of segments is mainly displaced at the scapular pivot or hip joint, both of which have the same vertical distance to the ground. Two Key words: in-phase gait, lumbar spine, locomotion, symmetrical segments operate in matched motion during retraction of gait, X-ray, small therian mammal. Introduction The evolution of mammalian limbs is marked by the transition from a two-segmented, sprawled tetrapod limb to a three-segmented limb (for a review, see Fischer, 1999) and from lateromedial, undulatory movements to dorsoventral movements of the body axis (Hildebrand, 1974). The addition of locomotory active segments is achieved in different ways for fore- and hindlimbs: the shoulder blade becomes moveable and is added as the proximal segment to the ‘old’ ancestral forelimb (Jenkins and Weijs, 1979), whereas on the hindlimb the existing distal element, the foot, is prolonged and becomes the third segment by the ‘new’ ankle joint. As a consequence serially homologous elements such as humerus and femur no longer functionally correspond to each other. The functional correspondence is now: shoulder blade to thigh, upper arm to lower limb, forearm to foot. These postural changes influence fundamentally the action of the limbs during locomotion. Our first aim is to present quantitative kinematic data of fore- and hindlimbs’ movements for several, only distantly related, small therian mammals at different gaits. Based on this substantial amount of highly detailed work, a comparative study of limb configuration and kinematics was undertaken to look for basic kinematic similarities emerging together with the new therian limb. The principles that emerge from these studies, together with the published work especially on cats will be also tested for their validity in midsize ungulates. Another key innovation of therian locomotion is the regular use of in-phase gaits (gallop, half-bound, bound); crocodiles show gallop only exceptionally as juveniles (Zug, 1974). According to Hildebrand (1985), sagittal spine movements occur typically in fast carnivores, lagomorphs, and rodents. We present first data for other especially small therians. The consequences of these ‘new’ gaits on fore- and hindlimbs and especially lower spine kinematics have never been quantified using cineradiography. Based on the X-ray study of slow walking (i.e. exploratory walking) in the tree shrew Tupaia glis, a restricted bending region of flexion between Th11 and L1 has been described (Jenkins, 1974a). This observation will be tested in faster ‘in-phase’ gaits. In our study, we also included animals with and without tails, to test their influence on the kinematics of the sagittal back movements. Cineradiography is the only tool that recognizes the exact kinematics of all proximal skeletal parts hidden under the skin and subcutaneous fat. Previous studies on quadrupedal therian mammals quantitatively analysed either (1) single joints such 1316 M. S. Fischer and others as the shoulder joint in rats (Rattus norvegicus; Jenkins, 1974b), hip joint and back movements in the skunk (Mephitis mephitis; Van de Graaff et al., 1982), trunk movements in the shrew-like opossum (Monodelphis domestica; Pridmore, 1992), elbow and wrist joint in the potto (Perodicticus potto; Jouffroy et al., 1983), ankle joint in kangaroo rats (Dipodomys spectabilis; Biewener and Blickhan, 1988), single limbs at specific gaits (e.g. hindlimb in cats Felis catus f. domestica; Kuhtz-Buschbeck, 1994), or (2) qualitatively single steps only at one or more gaits (e.g. Tupaia; Jenkins, 1974a; jirds Meriones shawi; Gasc, 1993). Most data are available for the cat, which has long been used as a model organism (Engberg and Lundberg, 1969; Goslow et al., 1973; Miller and Van der Meché, 1975; Jenkins and Camazine, 1977; Sontag et al., 1978; English, 1978a,b, 1980; Halbertsma, 1983; Hoy and Zernicke, 1985; Caliebe et al., 1991; Kuhtz-Buschbeck et al., 1994; Boczek-Funcke et al., 1996, 1998, 1999). From outside of our group the only cineradiographic study on fore- and hindlimb kinematics at different gaits was published by Rocha Barbosa et al. (1996) on the domestic guinea pig Cavia porcellus. Scapular displacement during quadrupedal locomotion has been measured in Felis (Miller and Van der Meché, 1975; English, 1978a; Sontag et al., 1978; Boczek-Funcke et al., 1996), Rattus (Jenkins, 1974b), Cavia (Rocha Barbosa et al., 1996), Virginia opossum, Didelphis marsupialis (Jenkins and Weijs, 1979) and vervet monkeys Cercopithecus aethiops (Roberts, 1974; Whitehead and Larson, 1994). The studies named describe a clear pro- and retraction of the shoulder blade during locomotion, but the impact of this displacement on step length and the overall kinematics of the forelimb has never been determined. We have collected kinematic data on eight different small therian mammals using cineradiography. Data of two phylogenetically distant metatherians (Dasyuroides byrnei, Monodelphis domestica) and six eutherians belonging to five different orders (Primates: Microcebus murinus; Rodentia: Galea musteloides, Rattus norvegicus; Lagomorpha: Ochotona rufescens; Hyracoidea: Procavia capensis; Scandentia: Tupaia glis) are now available to elaborate upon the kinematic principles of small mammal locomotion. In addition, data based on analyses of two artiodactyls, Tragulus javanicus and the domestic goat Capra hircus (Lilje and Fischer, 2001), a very small rodent (Acomys cahirinus), as well as another primate (Saguinus oedipus; Schmidt and Voges, 2001) are included in this paper (e.g. in illustrating touch-down and liftoff positions). Single kinematic studies including detailed information about metric parameters, footfall patterns and gaitspecific kinematics, as well as intralimb timing are already published on Procavia capensis (Fischer, 1994, 1998), Ochotona rufescens (Fischer and Lehmann, 1998), Tupaia glis (Schilling and Fischer, 1999), and Eulemur fulvus (Schmidt and Fischer, 2000). These published data are drawn together here by further calculations, for example, on the contribution of limb segments to step length. Materials and methods Animals Limb kinematics were studied by cineradiography in adult individuals of eight small therian species which belong to different higher-order taxonomic groups of mammals. The kinematic analyses are based on more than 80,000 digitised Xray frames. Table 1 gives an overview of the species under investigation by denoting number of individuals, body mass and body length. For sake of simplicity, we named the species by their generic names only. All experiments were registered by the Committee for Animal Protection of the State of Thuringia, Germany. Individuals were positively conditioned to move on a horizontal motor-driven treadmill within a Plexiglas enclosure (length 100 cm, width and height were adapted to the requirements of each species) except for the arboreal quadrupedal Microcebus, which walked on a rope-mill, an arboreal analogue of a treadmill. Treadmill speed was not fixed, but the operator attempted to keep the running animal in front of the X-ray screen for as long as possible. Thus, the operator adjusted the speed to obtain certain preferred speeds of the animals. Comparisons of treadmill locomotion and unrestrained locomotion have shown that the basic schemes of kinematics are the same in both situations (Fischer, 1999). Cineradiography The X-ray equipment consisted of an automatic Philips unit (Type 9807 501800 01) with one X-ray source image-amplifier chain. Pulsed X-ray shots were applied Table 1. Number, size characteristics of the eight species under study Number of individuals Males Monodelphis domestica (Metatheria) Dasyuroides byrnei (Metatheria) Galea musteloides (Rodentia) Rattus norvegicus (Rodentia) Ochotona rufescens (Lagomorpha) Procavia capensis (Hyracoidea) Tupaia glis (Scandentia) Microcebus murinus (Primates) 2 2 1 2 2 2 1 1 Females 1 1 1 Body mass (g) Snouth–vent length (mm) 92 145 300 350 250 1200 180 100 82 145 216 205 191 280 189 130 Limb kinematics of small mammals 1317 (approximately 50 kV, 200 mA). The X-ray images on the image intensifier were recorded either on 35 mm film using an Arritechno R35-150 camera or with a high-speed CCD camera (Mikromak Camsys) operating at 150 frames s–1. The animals were filmed in a lateral projection with a maximum exposure time of 10 s. As some of the animals were larger than the area of interest covered by the image-amplifier (20.5 cm×15.0 cm), fore- and hindlimbs were recorded separately. An orthogonal wire grid, perpendicular to the projection plane, provided reference points for correction of geometrical distortions and metrical calculations. at the flexor side of each joint. Segment angles were calculated versus the horizontal plane. We shall use the term protraction (= cranial rotation) for the cranial displacement of the distal end of each segment. Retraction (= caudal rotation) describes its caudal displacement. Maximum amplitudes of joint excursion during stance and swing phases were calculated from the initial moments of segment and limb-joint movements. Effective angular displacements (EAD) were defined as differences of angles at touch-down and lift-off. The ratio EAD versus maximum joint amplitudes gives the coefficient of stance phase (CSP). A ratio higher than 0.5 indicates a joint’s action resulting in a forward propulsive movement. Fischer and Lehmann (1998) proposed an ‘overlay method’ to calculate the relative contribution of angular movements to step length. While the CSP indicates the non-propulsive vertical work of joints, only the overlay method enables calculation of the relative contribution of segment movements to horizontal forward motion, because it considers the displacements of pivots of the limb segments during stance phase. Summarising the ‘overlay method’ in short, the calculations are based on mean values of typical gait sequences, of which stance and swing phase duration are scaled to equivalent relative durations using the method of linear interpolation. A polynomial fit of sixth order is used to interpolate data. For calculation, angular values are defined in the vertical plane to be positive if the distal end of the segment is in front of the proximal end. The horizontal distance (lp) between tip of toe and the pivot of the whole limb is determined for every single limb configuration during stance phase, using the lengths of segments and their angular excursions against the vertical plane. By overlaying the proximal segment onto the next configuration, without changing angles in the more distal joints, the difference between the horizontal excursion at instant i (lpi) and at instant i+1 (lpi+1) is the step length caused by the rotation of each particular segment. For each segment the absolute contribution to step length is given by the summation of all Processing of X-ray images X-ray films were copied onto video tapes and A/D-converted using a video processing board (Screen Machine I, Fast Multimedia AG, Munich, Germany), and further analysed by application of the software ‘Unimark 3.6’ (by R. Voss). This software makes it possible to digitise interactively previously defined landmarks with a cursor function; it also corrects distortions automatically and calculate angles and distances. The positions of digitised landmarks and angles calculated in the parasagittal plane are illustrated in Fig. 1. Angles calculated are the projections of angles onto the sagittal plane representing their contribution to movements in the plane of forward motion. The errors generated by digitisation of skeletal landmarks and their influence on the angles calculated were tested by repetitive digitisation (five times) of one sequence (25 frames) for each species. The digitisation error depends on the size of the animal and the image contrast of skeletal elements. It ranges from 0.5 ° to 2.0 ° for segment angles (see below) and is roughly 1.0–3.0 ° for joint angles, because the errors of two adjacent segment angles combine in joints following the Gaussian rules of error propagation. Analysis of angular movements and their contribution to step length Limb joint angles were defined anatomically and measured Pelvis Hip joint Scapula Shoulder joint Thigh Humerus Knee joint Elbow joint Ankle joint Lower arm Wrist joint Hand Joint angles Lower leg Segments to horizontal line 5 cm Fig. 1. Positions of captured skeletal landmarks and calculated angles of segments and joints projected onto the parasagittal plane. 1318 M. S. Fischer and others Table 2. Kinematic parameters of forelimb segments and limb joint angles at (A) symmetrical and (B) in-phase gaits Touch down angle (degrees) (A) Symmetrical gaits Scapula Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Humerus Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Lower arm Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Hand Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Shoulder joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Elbow joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Wrist joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Procavia capensis Tupaia glis Microcebus murinus Lift-off angle (degrees) Amplitude stance (degrees) Mean Range N Mean Range N Mean Range N Contribution to step length (%) 37 41 39 41 51 38 41 29–42 30–58 32–48 32–51 39–66 26–49 27–59 18 23 27 27 44 31 76 90 79 96 95 101 92 87 75–106 71–92 85–104 79–103 83–120 81–103 73–104 17 22 29 31 44 31 92 59 44 60 60 53 59 48 50–72 28–63 51–69 44–68 22–80 40–69 36–64 16 22 27 27 44 28 76 53 58 73 57 63 43 46 62 36 62 58 65 85 78 39–76 16–68 38–73 51–70 25–97 65–102 52–103 18 23 27 27 47 31 76 –20 –21 –7 –18 –2 –12 –5 –29–14 –44–9 –14–0 –28–4 –16–16 –24–2 –26–9 17 22 28 31 47 31 92 84 59 71 78 83 105 87 69–96 37–91 59–82 63–94 48–113 88–134 64–105 16 22 27 27 15 28 76 25 15 11 16 18 17 27 24 36 30 24 28 8 11 14–35 24–46 25–35 18–33 10–47 1–15 4–39 18 23 26 27 47 31 72 120 107 122 120 117 138 112 88–135 84–133 112–131 106–130 93–138 101–156 95–128 17 22 27 29 47 31 84 96 72 94 100 100 133 102 80–116 53–109 87–105 84–110 68–122 99–152 82–121 16 22 26 27 15 28 72 16 22 15 18 18 32 20 10 12 33 16 40 13 2 3–24 0–22 25–46 5–26 18–67 4–22 −13–16 18 23 26 27 45 31 59 104 86 119 143 133 157 75 64–154 41–125 96–155 107–178 103–153 109–193 23–128 17 22 27 29 45 31 84 103 80 95 132 100 153 78 59–154 37–115 70–122 93–162 77–130 97–192 34–136 16 22 26 27 15 28 58 6 5 1 9 1 8 7 99 75 101 99 115 123 120 77–113 51–101 91–110 89–110 88–138 105–141 93–141 18 23 27 27 44 31 76 71 59 89 77 100 80 82 58–88 37–73 79–99 57–89 72–121 58–98 64–98 17 22 28 31 44 31 92 47 29 23 38 30 60 49 30–62 9–51 16–32 25–52 11–53 40–89 26–75 86 71 93 82 92 90 85 62–102 44–102 79–101 69–98 57–120 76–115 61–105 18 23 26 27 44 31 74 100 86 116 101 116 124 101 66–114 57–120 103–130 84–118 83–143 78–150 76–117 17 22 27 29 44 31 89 41 37 42 44 45 70 40 194 205 186 188 168 176 187 178–203 192–224 181–199 177–200 150–183 163–186 172–201 18 23 26 27 39 31 63 196 201 193 157 162 154 215 114–234 166–251 181–222 115–197 139–191 100–191 168–248 17 22 27 29 39 31 89 71 53 37 92 25 86 76 Coefficient of stance Mean N 16 22 27 27 44 28 75 0.62 0.56 0.50 0.56 0.53 0.70 0.86 16 22 27 27 44 28 75 25–55 14–65 35–53 26–55 14–71 30–93 24–61 16 22 26 27 44 28 74 0.35 0.49 0.55 0.46 0.55 0.47 0.38 16 22 26 27 44 28 72 43–133 33–82 26–49 55–127 8–49 43–142 46–109 16 22 26 27 39 28 63 0.25 0.45 0.25 0.34 0.59 0.25 0.42 16 22 26 27 39 28 57 Limb kinematics of small mammals 1319 Table 2. Continued Touch down angle (degrees) (B) In-phase gaits Scapula Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Humerus Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Lower arm Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Hand Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Shoulder joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Elbow joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Wrist joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Lift-off angle (degrees) Amplitude stance (degrees) Mean Range N Mean Range N Mean Range N Contribution to step length (%) 42 45 47 46 54 46 29–61 33–64 39–57 20–70 45–68 36–61 43 18 38 318 28 17 84 80 92 80 101 85 72–93 67–90 86–100 51–100 94–110 66–95 44 18 39 318 28 12 45 37 47 37 48 47 25–60 25–48 38–55 7–65 32–64 37–67 40 18 38 318 28 12 52 55 59 66 80 47 52 46 52 61 59 86 8–80 43 22–64 18 42–62 38 20–89 316 30–87 31 63–106 17 –23 –11 –3 –1 9 –13 –35–13 –25–5 –13–4 –24–23 –3–16 –31–2 44 18 39 316 31 12 78 59 60 62 36 100 28–104 36–85 49–76 20–101 26–59 72–128 40 18 38 316 8 12 26 25 10 23 –9 45 25 45 39 33 46 18 8–41 32–59 24–52 12–61 26–62 6–28 43 18 38 316 31 17 112 111 128 96 118 105 94–128 102–123 119–135 57–123 97–127 88–124 44 18 39 316 31 12 88 66 89 64 68 87 73–107 48–77 67–101 23–96 56–82 80–101 40 18 38 316 8 12 19 13 27 8 29 3 4 36 29 14 52 17 –7–16 20–62 12–47 –2–56 32–85 10–28 39 18 38 316 31 12 65 130 134 86 132 136 2–120 97–152 107–159 21–157 114–143 114–156 44 18 39 316 31 12 64 97 109 75 70 126 8–118 66–130 81–141 17–154 58–94 100–147 36 18 38 316 8 9 3 7 4 3 0 5 94 91 99 107 114 132 66–126 43 61–113 18 91–110 38 80–140 318 90–136 28 107–153 17 61 69 89 80 110 72 47–75 46–91 80–95 50–105 101–117 62–82 44 18 39 318 28 12 40 29 26 30 23 60 7–70 10–48 15–37 1–63 10–37 31–91 77 91 91 94 106 104 43–103 43 69–108 18 82–98 38 68–120 318 81–130 28 82–124 17 89 101 125 96 127 91 62–108 86–116 108–137 60–120 104–136 65–107 44 18 39 318 28 12 43 28 54 20 38 41 202 188 190 200 175 183 181–217 43 163–202 18 171–210 38 159–235 318 152–185 28 167–198 13 227 165 174 190 165 149 164–297 139–205 152–200 102–255 147–177 115–174 44 18 39 318 28 12 62 43 51 42 24 72 single-frame calculations in stance phase. Finally, the contribution of the remaining segments to forward motion is calculated in the same way, except for the subtraction of the angular movement achieved by the sagittal rotation of the Coefficient of stance Mean N 40 18 38 318 28 12 0.82 0.74 0.96 0.91 0.5 0.98 40 18 38 318 28 12 28–58 6–42 32–73 0–45 18–55 24–62 40 18 38 318 28 12 0.39 0.45 0.62 0.51 0.53 0.46 40 18 38 318 28 12 42–91 19–80 28–71 2–127 8–37 51–112 36 18 38 318 28 9 0.56 0.65 0.36 0.49 0.49 0.46 40 18 38 318 28 9 more proximal segment(s). The relative contribution of segment displacement to step length depends on the pivot’s height, the effective angular displacement (EAD) and the length of the segment. 1320 M. S. Fischer and others Results Fore- and hindlimb kinematics were studied by cineradiography in eight small therian species. At least 15, but up to 300, step cycles (period between two successive touchdowns of one limb) were analysed within broad ranges of running speeds (Galea, 0.3–1.3 m s–1, Dasyuroides, 0.3–1.0 m s–1, Microcebus, 0.3–1.7 m s–1, Monodelphis, 0.4–2.4 m s–1, Procavia, 0.2–2.1 m s–1, Ochotona, –1 0.2–1.6 m s , Rattus, 0.4–0.8 m s–1, Tupaia, 0.5–1.6 m s–1). Each species preferred different gaits within even the same speed ranges; e.g. Rattus and Microcebus only used ‘walk’ but pikas only used ‘halfbound’ and ‘gallop’. Because most animals changed both frequently and suddenly between walk and trot, or gallop and halfbound, we pooled walk and trot data as symmetrical gaits, as well as gallop and halfbound as inphase gaits. Kinematic data comprise segment and joint angles at touchdown and lift-off, maximum amplitude of the stance phase, contribution of segment displacement to step length and the coefficient of stance for limb joints at symmetrical gaits (Tables 2A, 3A) and in-phase gaits (Tables 2B, 3B,C). Differences between trailing and leading limbs (first and second touch-down) were observed on the hindlimbs only at gallop and half bound and therefore, these limbs are presented separately. The following description of the kinematics of small mammalian locomotion is divided into three main parts: forelimb, spine movement, and hindlimb. The sections on limb kinematics start with the displacement pattern of the limb segments and their contribution to step length, followed by the description of joint movements. Forelimb Kinematics of forelimb segments Segment displacements consist mainly of retraction during the stance phase and protraction during the swing phase. In all species, retraction of all segments starts before touch-down at 90–95 % of the previous step cycle duration at symmetrical gaits and at 80 % of the previous step duration at in-phase gaits (Fig. 2A,B). Scapular protraction begins at 85–90 % of stance duration at symmetrical gaits but its timing is more variable at in-phase gaits. The beginning of humeral protraction varies around lift-off at all gaits, whereas forearm protraction is timed to coincide with lift-off at symmetrical gaits or with 10 % of swing duration at in-phase gaits. Protraction of the hands begins late in the first third of swing. Fig. 2A,B illustrates the high uniformity of segment displacements (except of the hand) in all species. Forelimb protraction and retraction are executed mainly by scapular displacement, as the most proximal segment. Retraction of the scapula begins from the most flexed position at 35–40 ° in the late swing phase. Mean touch-down angles of the scapula range within 37–51 ° at symmetrical gaits and 42–54 ° at in-phase gaits. In those species in which symmetrical as well as in-phase gaits could be analysed, an increased scapular touch-down angle was observed at in-phase gaits. A continuous retraction of the scapula leads to a nearly vertical orientation at the end of stance. Rotary movement then stops and in aclaviculate species such as Procavia, a translatory gliding along the thoracic wall follows (for details, see Fischer, 1994). Mean scapular lift-off angles are between 79 ° and 101 ° at symmetrical gaits and are in approximately the same range at in-phase gaits (Table 2A,B). Mean amplitudes of scapular retraction are maximally 10 % higher than the differences of angles at touch-down and lift-off. The greatest amplitude of scapular retraction was measured in the rodents (60 ° for both species) and in Monodelphis and Tupaia, each with 59 °. In all species, humeral displacement is as uniform as scapular movement (Fig. 2A,B). Mean touch-down angles for five species are in a small range of less than 10 ° (58–65 ° at symmetrical gaits, 52–61 ° at in-phase gaits). Tupaia and Microcebus have a more protracted upper arm at touch-down with mean angles of 85 ° and 78 °, respectively (Fig. 4). In contrast, Dasyuroides has the most retracted humerus at touchdown, being only 36 ° at symmetrical gaits and 46 ° at in-phase gaits. This species also shows the lowest overall amplitude of humeral displacement at 59 ° and Tupaia the highest amplitude of humeral retraction at 105 ° (Table 2A). Retraction of the humerus starts before touch-down and is already completed at midstance. Afterwards, the humerus is positioned more or less horizontally and held in this position until the first quarter of the swing phase (Procavia –2 °, Galea –7 ° and Microcebus –5 ° at symmetrical gaits; Procavia 9 °, Galea –3 ° and Ochotona –1 ° at in-phase gaits). Monodelphis, Dasyuroides and Rattus elevate the humerus more above the horizontal line (mean angle between –18 ° and –21 ° at symmetrical gaits). The forearm is in matched motion with the scapula (i.e. both segments are displaced nearly parallel to each other), especially during the stance phase (Fig. 2B). Mean touch-down angle is highly uniform at symmetrical gaits and ranges between 24 ° and 36 ° with the exception of Tupaia (8 °) and Microcebus (11 °) in which – by stronger protraction of the humerus and not by elbow flexion (see below) – the forearm is placed almost parallel to the ground. At in-phase gaits, the mean touch-down angle is more variable within our sample of species and lies between 18 ° in Tupaia and 46 ° in Procavia. Retraction of the forearm continues until the end of stance phase and ends at lift-off at symmetrical gaits, or at 10 % of the swing phase at in-phase gaits. Lift-off angle varies slightly between species (107–122 °) at symmetrical gaits. Only Tupaia deviates from this position with a more retracted forearm (138 °) and thus has the greatest overall amplitude of forearm movement (133 °). The mean lift-off angle has a broader range at in-phase gaits. The lowest values were observed in Ochotona (96 °) and Tupaia (105 °), whereas Galea has the highest lift-off angle at 128 °. The hand is placed in a semidigitigrad position; a digitigrad position was frequently observed only in Procavia. In Microcebus, walking on a rope-mill, the hand grasps around the circumference of the rope. Here, hand and wrist joint angles also were projected onto the sagittal plane. Hand displacements Limb kinematics of small mammals 1321 Table 3. Kinematic parameters of hindlimb segments and limb joint angles at (A) symmetrical and (B,C) in-phase gaits. Trailing and leading limbs are presented separately in (B) and (C) respectively Touch down angle (degrees) Lift-off angle (degrees) Amplitude stance (degrees) Range N Contribution to step length (%) 12 17 10 7 10 14 13 14 5–25 8–32 6–18 4–11 6–19 5–31 6–23 7–28 16 19 47 23 29 21 30 76 –3 7 3 –3 4 7 2 10 16 19 76 27 30 22 33 85 84 51 76 60 51 71 110 78 70–101 24–85 59–101 45–84 36–69 55–83 91–126 40–98 16 19 74 23 29 11 29 75 93 59 84 69 67 52 82 93 3–21 –9–9 –26–7 –17–5 –6–7 –14–6 –20–11 –5–33 16 19 76 27 30 22 33 76 71 61 55 77 66 93 59 71 60–81 46–85 43–64 69–84 51–76 82–103 48–76 56–98 16 19 74 23 29 11 29 75 –1 15 –9 18 19 26 –21 –7 105 92 117 102 91 137 138 109 80–139 67–118 99–130 77–118 71–103 103–165 128–151 86–132 14 19 74 26 30 22 31 77 97 81 105 95 80 124 129 95 74–131 46–118 85–121 79–110 59–98 103–144 114–150 87–124 13 19 72 23 29 11 29 67 11 19 22 16 10 15 37 4 18 21 47 25 30 21 33 76 123 73 115 102 96 107 141 113 98–141 40–98 103–126 93–109 86–106 86–139 116–156 85–135 16 19 48 27 30 21 33 85 86 46 75 60 49 70 110 75 70–103 18–80 59–88 45–78 29–60 50–100 92–123 56–92 78–104 18 47–84 21 56–74 75 61–93 25 66–87 30 57–96 21 52–79 33 68–109 76 106 49 86 63 61 58 124 92 74–127 24–86 67–109 53–74 53–71 24–96 82–151 60–129 16 19 76 27 30 21 33 85 44 25 28 24 21 45 72 30 28–58 9–49 11–52 13–34 11–34 30–63 44–100 15–54 Mean Range N Mean Range N Mean (A) Symmetrical gaits Pelvis Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 33 28 22 36 37 51 19 42 21–42 5–45 14–29 32–43 28–47 36–68 9–30 25–60 18 21 47 25 30 21 33 77 31 23 19 35 35 47 16 37 21–39 9–31 14–27 28–43 30–42 30–60 6–27 26–49 16 19 48 27 30 21 33 86 Thigh Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 8 3 24 7 14 –7 16 1 0–20 –15–26 10–37 -4–14 –2–22 –18–4 2–29 –12–27 18 21 75 25 30 22 33 76 92 51 100 66 61 60 125 76 59–109 14–89 83–116 58–76 49–70 30–95 102–143 53–96 Lower leg Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 84 59 41 73 65 82 49 87 69–96 37–76 29–53 63–84 56–72 66–101 33–60 63–98 18 21 75 25 30 22 33 76 14 –2 –14 –3 –1 –4 –1 16 Foot Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 7 13 12 8 11 18 9 16 –1–14 –3–33 5–23 –4–15 2–17 7–35 –1–17 1–47 18 21 73 24 30 22 32 77 Hip joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 41 31 40 43 51 45 35 43 32–48 21–51 34–47 28–54 44–61 29–56 27–46 27–54 Knee joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus 92 62 65 79 79 76 65 88 Coefficient of stance Mean N 16 19 47 23 29 21 30 75 0.96 0.9 0.99 0.96 0.99 0.89 0.96 0.9 16 19 47 23 7 21 30 75 16 19 74 23 29 21 30 75 0.42 0.67 0.73 0.73 0.32 0.52 0.8 0.4 16 19 74 23 7 21 30 75 1322 M. S. Fischer and others Table 3. Continued Touch down angle (degrees) (A) Symmetrical gaits Ankle joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Rattus norvegicus Ochotona rufescens Procavia capensis Tupaia glis Microcebus murinus Lift-off angle (degrees) Amplitude stance (degrees) Contribution to step length (%) Mean Range N Mean Range N Mean Range N 91 72 53 81 76 101 58 103 74–104 51–93 46–60 70–88 71–83 84–115 47–70 84–126 18 21 73 24 30 21 32 77 118 91 103 99 90 133 137 125 83–151 66–124 84–120 75–121 75–106 102–167 108–151 98–165 13 19 74 26 30 21 31 77 66 34 53 36 30 60 88 36 32–102 14–68 32–72 22–48 17–39 24–98 60–107 20–74 13 19 72 23 29 21 29 67 36–55 45–59 45–66 46–85 58–93 27–60 42 11 16 107 51 14 3 13 13 49 37 11 –7–11 6–22 6–23 32–78 27–65 4–25 34 10 17 107 51 14 44 40 44 27 49 35 30–55 29–51 23–67 3–45 23–64 18–52 32 10 16 107 50 14 52 52 50 53 49 45 –26–31 –16–11 –18–8 –13–14 –31–1 –22–22 42 11 16 107 50 14 98 63 86 47 56 101 69–122 34 53–72 11 67–105 17 12–83 107 10–82 50 60–120 14 98 70 88 50 86 97 61–133 32 50–85 11 66–123 16 15–87 107 77–97 10 52–119 14 47 29 36 8 16 46 64–98 42 65–94 11 55–95 16 54–102 107 81–113 50 45–72 14 21 7 –19 18 3 –11 1–41 1–15 –25–10 1–36 –13–40 –18––1 34 11 17 107 50 14 67 74 90 65 107 70 31–95 32 57–91 11 75–112 16 37–92 107 100–115 10 54–94 14 –10 5 6 35 25 –7 –9–30 –2–27 –1–13 –3–29 0–48 4–19 42 11 16 107 48 14 98 109 110 78 121 107 63–135 34 103–114 7 93–128 17 17–125 107 54–147 50 65–120 11 94 97 105 73 128 95 60–128 32 76–112 7 91–129 16 14–121 107 121–138 10 52–112 11 11 14 8 4 10 16 23–67 37–63 45–64 49–92 45–94 38–56 42 11 16 107 50 14 101 77 99 95 93 112 79–128 34 68–84 9 90–111 17 68–120 107 51–114 50 85–127 14 56 33 50 26 38 64 33–82 21–41 39–71 5–60 20–69 35–78 62–111 42 66–88 11 62–79 16 61–104 107 42–111 51 48–73 14 119 70 67 64 59 91 76–149 34 60–80 11 48–93 17 40–109 107 19–95 51 60–109 14 54 32 27 34 65 45 34–87 21–50 11–51 6–55 42–98 15–60 67–116 78–106 119 117 74 40 39–133 28–48 (B) In-phase gaits, trailing limb Pelvis Monodelphis domestica 46 Dasyuroides byrnei 53 Galea musteloides 56 Ochotona rufescens 73 Procavia capensis 78 Tupaia glis 45 Thigh Monodelphis domestica 0 Dasyuroides byrnei –6 Galea musteloides –1 Ochotona rufescens 1 Procavia capensis –9 Tupaia glis 5 Lower leg Monodelphis domestica 85 Dasyuroides byrnei 81 Galea musteloides 71 Ochotona rufescens 82 Procavia capensis 100 Tupaia glis 56 Foot Monodelphis domestica 7 Dasyuroides byrnei 9 Galea musteloides 5 Ochotona rufescens 8 Procavia capensis 16 Tupaia glis 12 Hip joint Monodelphis domestica 46 Dasyuroides byrnei 47 Galea musteloides 55 Ochotona rufescens 74 Procavia capensis 67 Tupaia glis 49 Knee joint Monodelphis domestica 85 Dasyuroides byrnei 75 Galea musteloides 69 Ochotona rufescens 83 Procavia capensis 89 Tupaia glis 61 Ankle joint Monodelphis domestica 91 Dasyuroides byrnei 90 42 11 84–163 112–120 34 7 Coefficient of stance Mean N 0.42 0.57 0.94 0.48 0.57 0.53 0.9 0.7 13 19 72 23 7 21 29 67 32 9 16 107 49 14 0.95 0.88 0.9 0.78 0.7 0.98 32 9 16 107 49 14 32 11 16 107 50 14 0.6 0.28 0.34 0.57 0.46 0.69 32 11 16 107 50 14 32 7 0.37 0.67 32 7 Limb kinematics of small mammals 1323 Table 3. Continued Touch down angle (degrees) Mean Range Lift-off angle (degrees) N Amplitude stance (degrees) Mean Range N Mean Range N 91 97 125 94 68–114 55–134 92–150 64–110 17 107 51 12 42 35 63 40 25–67 12–70 33–87 12–58 16 107 48 12 Contribution to step length (%) Coefficient of stance Mean N 0.36 0.44 0.27 0.67 16 107 48 12 (B) In-phase gaits, trailing limb Galea musteloides 76 Ochotona rufescens 90 Procavia capensis 115 Tupaia glis 69 64–94 16 57–130 107 88–152 49 59–78 14 (C) In-phase gaits, leading limb Pelvis Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis 46 52 50 73 80 38 36–55 45–58 34–72 45–92 59–92 19–56 42 11 16 104 18 14 3 12 9 43 40 2 –7–11 4–21 3–17 30–78 29–65 –9–9 34 10 16 104 18 12 44 40 41 31 46 39 30–55 29–53 18–64 0–51 23–62 28–58 32 10 16 104 17 13 53 51 38 65 48 41 Thigh Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis 0 –5 –5 –9 –14 0 –26–31 –14–9 –21–11 –27–27 –29–1 –21–18 42 11 16 104 12 14 98 70 98 52 67 109 69–122 44–111 88–107 25–76 10–95 83–124 34 11 16 104 12 13 98 75 103 61 103 109 61–133 39–125 83–125 23–100 70–132 74–127 32 11 16 104 9 13 44 28 50 10 27 53 Lower leg Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis 85 80 71 82 98 61 64–98 42 68–96 11 60–87 16 49–98 104 71–109 13 34–78 14 21 12 –14 22 6 –4 1–41 0–39 –27–6 4–46 –14–14 –20–10 34 11 16 104 13 13 67 71 86 60 107 71 31–95 57–87 64–105 19–89 96–116 49–87 32 11 16 104 9 13 –8 7 2 19 16 –12 Foot Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis 7 7 4 5 19 10 –9–30 –1–17 1–7 –7–29 5–50 2–20 42 11 16 104 12 14 98 103 118 81 126 114 63–135 81–114 107–132 9–118 97–142 82–141 34 7 16 104 13 12 94 94 115 77 122 104 60–128 81–106 95–131 23–114 105–150 74–131 32 7 16 104 9 12 11 14 11 6 9 18 46 47 44 64 60 38 23–67 39–59 26–63 44–78 40–80 32–48 42 11 16 104 40 14 101 80 106 94 109 110 79–128 60–115 97–116 67–124 71–141 87–123 34 10 16 104 38 12 56 36 68 33 61 72 33–82 11–72 43–84 6–73 24–95 46–88 32 10 16 104 37 12 0.95 0.91 0.92 0.89 0.74 0.99 32 10 16 104 37 12 85 75 66 73 75 75 62–111 42 67–86 11 50–84 16 46–94 104 42–100 39 36–126 13 119 74 84 74 79 91 76–149 60–88 62–97 53–108 19–104 58–129 34 10 16 104 39 13 54 31 36 22 61 57 34–87 18–48 24–52 5–58 40–87 24–79 32 10 16 104 38 13 0.6 0.41 0.50 0.56 0.3 0.76 32 10 16 104 38 13 91 87 75 87 110 71 67–116 42 76–98 11 62–90 16 68–115 104 76–147 39 53–86 14 119 113 104 104 134 110 84–163 97–123 80–125 60–137 77–161 80–144 34 7 16 104 39 12 74 40 54 35 70 54 39–133 23–49 32–74 4–70 51–99 28–86 32 7 16 104 38 12 0.37 0.67 0.55 0.54 0.37 0.7 32 7 16 104 38 12 Hip joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Knee joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis Ankle joint Monodelphis domestica Dasyuroides byrnei Galea musteloides Ochotona rufescens Procavia capensis Tupaia glis 1324 M. S. Fischer and others A Forelimb, walk Lift-off 100 90 80 70 60 50 40 30 20 120 Lift-off 140 130 120 110 100 90 80 70 60 50 40 150 Scapula Upper arm 100 Shoulder joint Elbow joint 130 80 110 Angle (degrees) 60 40 90 20 70 0 50 –20 –40 160 140 120 100 80 60 40 20 0 –20 200 180 160 140 120 100 80 60 40 20 0 –20 30 260 240 220 200 180 160 140 120 100 80 Forearm Hand Wrist joint 0 20 40 60 Step duration (%) 80 100 Monodelphis domestica Dasyuroides byrnei Procavia capensis Galea musteloides Rattus norvegicus 0 20 40 60 Step duration (%) 80 100 Tupaia glis Microcebus murinus Fig. 2. Mean values of forelimb segment angular excursions of typical sequences at symmetrical (A) and in-phase (B) gaits. Stance and swing phases are scaled to the same duration using the method of linear interpolation. Based on this method the data for each limb segment are smoothed but their characteristics are preserved. Note the uniformity of time schemes especially of segment displacements despite differences for example in shoulder joint angular excursions. are highly variable between all species as compared to the relative uniformity of displacements of the more proximal segments. Mean touch-down angles vary within broad ranges (2–40 ° at symmetrical gaits, 4–52 ° at in-phase gaits). The highest angle value was measured in Procavia (Table 2A,B), in which the hand is displaced in a line with the forearm and synchronised with it at the start of retraction and protraction (Fig. 2A,B). Hand retraction starts in the second half of the stance phase and ends in the first third of the swing phase in all species except Procavia. Mean lift-off angles are between 78 ° (Microcebus) and 157 ° (Tupaia) at symmetrical gaits, but at in-phase gaits Tupaia (136 °), are closer to the values Limb kinematics of small mammals 1325 B Forelimb, in-phase gaits Lift-off 100 Lift-off 160 Scapula 90 140 80 120 70 Shoulder joint 100 60 80 50 40 60 30 40 20 120 20 140 Upper arm 100 Elbow joint 120 80 60 100 40 80 Angle (degrees) 20 60 0 40 –20 –40 140 20 260 Forearm 120 240 100 220 200 80 60 180 160 40 140 20 120 100 0 180 160 140 120 100 80 60 40 20 0 –20 Hand Wrist joint 0 20 40 60 Step duration (%) 80 100 Monodelphis domestica Dasyuroides byrnei Ochotona rufescens Procavia capensis 0 20 40 60 Step duration (%) 80 100 observed in most other species (e.g. Galea 134 °, Dasyuroides 130 °, Procavia 132 °). Monodelphis shows a relatively lower angle at these gaits (65 °). Contribution of forelimb segment movements to step length The dissociation of segment and joint movements becomes obvious when the displacement of humerus, forearm and hand are compared with the effective angular movements in shoulder, elbow and wrist joints. Distal segments have a low degree of proper motion in the proximal adjacent joint and are Tupaia glis Galea musteloides driven passively by the action of the more proximal segments. For example, the proper motion of the humerus in the shoulder joint of Microcebus during the stance phase accounts for only 48 % of its amplitude. More than 50 % of its humeral displacement results from scapular retraction alone and only 25 % of its forearm displacement is actually achieved in the elbow joint. Calculation of the contribution of segment movements to step length using the ‘overlay method’ (Fischer and Lehmann, 1998) indicates the predominance of scapular retraction in 1326 M. S. Fischer and others forelimb movement. Scapular retraction accounts for more than 50 % and up to 80 % for step length in most species but for less than 50 % in Tupaia and Microcebus (Table 2A,B). The high value in Procavia (80 %) results from both the high scapular pivot and the amplitude at in-phase gaits. In contrast, the relative position of the scapular pivot in Dasyuroides is even higher than in Procavia (Fig. 4) but the amplitude of scapular retraction is low and, therefore, the overall contribution of the scapula is lower in Dasyuroides than in Procavia. The relatively lower scapular contribution in both Tupaia and Microcebus is due to an overall increase in step length, caused in the first instance by a stronger protraction of the humerus and additionally by an extensive retraction of the forearm in Tupaia. Except for these two species, the contribution of humeral displacement to step length is always less than half of the scapular amount. The forearm contributes positively to step length only in the second half of the stance phase when its pivot (the elbow) raises. The forearm’s contribution can exceed the value of the upper arm in species in which the forearm is retracted extensively; e.g. Tupaia at symmetrical gaits or Galea at in-phase gaits. The hand contributes to step length only in the last third of the stance phase when the wrist joint is lifted from the ground; in most species it contributes approximately 5 % and never more than 10 % to step length. Kinematics of forelimb joints In almost all species, the shoulder, elbow and wrist joints display biphasic angular movements during one step cycle for both symmetrical gaits and in-phase gaits (except for the wrist in Procavia and the shoulder in Tupaia; Fig. 2A,B). Phase relationships between different joints indicate that extensions in the shoulder, elbow and wrist joints are not synchronised. Flexion of all joints starts before touch-down, causing retraction of the segments. Flexion in the elbow joint reaches its maximum at 10–20 % of step duration (20–40 % of stance duration) (Fig. 2A,B), when the hand passes underneath the shoulder joint. Shoulder extension starts at midstance. The maximal dorsiflexion of the hand is reached at 65–70 % of stance duration. The second flexion of the shoulder joint coincides with the beginning of scapula protraction at the end of the stance phase. The elbow flexion initiates protraction of the forearms while maximum plantarflexion of the wrist joint occurs only in the first half of swing phase. The shoulder joint is the first joint to extend during the swing phase; elbow extension then follows at 50 % of the swing duration or later. An earlier extension of the elbow joint would counteract the forward movement of the limb. This sequence of forelimb joint movements during one step cycle is observed regularly in all species and at all gaits. Differences occur only in the degree of flexions and extensions, not in the intralimb coordination associated with the onset of movements. In contrast to the amplitude of segment displacement, the amplitude of angular excursions in limb joints can be twice as high as the difference between the angles at touch-down and lift-off (effective angular displacement, EAD), especially in the elbow and wrist joint (Tables 2A,B). The coefficient of stance phase (CSP), calculated as the ratio of EAD and the amplitude of joint excursion, indicates the degree of horizontal versus vertical action of joints. A CSP value of less than 0.5 indicates mainly vertically stretching and bending of the limbs and not to body protraction. The shoulder joint has a relative high CSP in all species. It ranges between 0.50 and 0.86 at symmetrical gaits and increases for most of the species at in-phase gaits (except for Procavia). Mean shoulder joint angles at touch-down range at symmetrical gaits from 75 ° in Dasyuroides to 123 ° in Tupaia, and are between 91 ° (Dasyuroides) and 132 ° (Tupaia) at inphase gaits (Table 2B). The mean lift-off angles are always smaller than touch-down angles and consequently, the resulting net joint movement of the shoulder joint is a flexion (except in Procavia at in-phase gaits). The variability of the lift-off angle is similar to that of the touch-down angle. In the first third of the stance phase, humeral retraction is faster than scapular caudal displacement, resulting in a flexion of the shoulder joint which ends at approximately 50 % of the stance duration. The flexion is rather weak in Procavia, Galea, Dasyuroides and Microcebus. Flexion diminishes at in-phase gaits, an effect which is pronounced in Monodelphis. Shoulder joint movement in Tupaia is exceptionally monophasic at inphase gaits, where the joint is continuously flexed during the whole of the stance phase and even until 26 % of swing duration (Fig. 2B). The lowest overall amplitude of shoulder movement was found at symmetrical gaits in Galea (23 °) and at in-phase gaits in Procavia (23 °), the highest in Tupaia (60 °). In almost all species, the amplitudes of elbow joint excursions during the stance phase occur within a small range (37–45 °) at symmetrical gaits (Table 2A). Only the amplitude of the elbow joint of Tupaia (70 °) deviates from these values, as a consequence of extensive retraction of the forearm at the end of the stance phase. At in-phase gaits, the amplitudes of elbow joint movements vary over a broader range, between 20 ° in Ochotona and 54 ° in Galea. Ochotona has both a reduced flexion at midstance and a reduced re-extension at the end of the stance phase (Fig. 2B). Compared to the shoulder joint, the net joint movement of the elbow joint is an extension in almost all of the animals we sampled at all gaits (except for Tupaia at in-phase gaits). The mean touch-down angle of the elbow joint is usually smaller than the lift-off angle and ranges from 71 ° in Dasyuroides to 93 ° in Galea at symmetrical gaits. At in-phase gaits, the lowest mean touch-down angle was measured in Monodelphis. In the other species, the mean angles increase to as much as 106 ° in Procavia. Compared to the shoulder and wrist joint, the mean touch-down angle of the elbow joint is more constant in all species and at all gaits. However, the range of the mean lift-off angle is higher (86–124 ° at symmetrical gaits, 89–127 ° at in-phase gaits). Tupaia shows the highest mean lift-off angles at symmetrical gaits (124 °), whereas the highest lift-off angles in Procavia (127 °) and Galea (125 °) occur at in-phase gaits. The lowest Limb kinematics of small mammals 1327 angle (86 °) was measured in Dasyuroides. The coefficient of stance of the elbow joint usually is lower than the CSP of the shoulder joint; mean values fall below 0.5 in Monodelphis, Dasyuroides, Rattus, Tupaia and Microcebus. In Ochotona and Procavia the CSP is 0.55. Only Galea shows a CSP of more than 0.6 at in-phase gaits. The range of the mean CSP of the wrist joint is similar to that of the elbow joint (Table 2A,B). The coefficient of stance in most species is below 0.5 at symmetrical gaits (0.25–0.45; Procavia 0.59), but it augments up to 0.36–0.65 at in-phase gaits. The mean touch-down angle of the wrist joint ranges between 168–205 ° at symmetrical gaits, but all species except for Procavia (175 °) show a dorsiflexion of the wrist joint (183–202 °) at in-phase gaits. Procavia deviates from the other species in our study by strongly reduced wrist joint excursions during the stance phase at all gaits (Fig. 2A,B). The hand is always displaced in line with the forearm owing to an anatomical restriction in the wrist joint (Fischer, 1998). The wrist joint of the other species is extended most during the last third of the stance phase, when the hand passes underneath the elbow joint. The amount of extension is much higher at symmetrical gaits (210–250 °). Amplitudes of wrist joint excursion during the stance phase decreases during in-phase gaits. Monodelphis is the only species that extends the wrist joint to a similar degree ( 250 °). The mean lift-off angle varies between 154 ° (Tupaia) and 215 ° (Microcebus) at symmetrical gaits and between 149 ° (Tupaia) and 227 ° (Monodelphis) at in-phase gaits. Spine movements Sagittal spine movements are the result of additive flexions and extensions between adjacent intervertebral joints in the lumbar vertebral column (Fischer, 1994; Fischer and Lehmann, 1998) or in the posterior thoracic and the lumbar vertebral column (Schilling and Fischer, 1999). Previous reports of a limited region of flexion and extension between Th11 and L1 in Tupaia (Jenkins, 1974a) have been validated only for exploratory walks (Schilling and Fischer, 1999). The additive effects of these movements lead to a displacement of the pelvis, and are called ‘pelvic movements’ in this study. Mobility within the iliosacral joint was not observed. Cranial and caudal ‘pelvic’ displacements are pronounced at in-phase gaits (Fig. 3B,C), in which the spine proves to be an important locomotory organ. Maximum cranial displacement is reached late during the swing phase and the subsequent caudal displacement continues until lift-off or even into the following swing phase. Mean touch-down angles are particular high in tail-less species, showing a nearly vertical pelvic position (e.g. Procavia, Ochotona). These angles are lower in the tailed animals (e.g. Monodelphis, Tupaia). At lift-off, the pelvis of tailed species is almost horizontal whereas in tail-less animals the pelvis is more inclined. So, tail-less species start at a more inclined position at the end of stance and reach an almost vertical position at the end of the swing, whereas species with rather long tails approach a horizontal position at lift-off but start much less inclined at stance (Fig. 4). The tail-less species Galea, however, behaves like the two latter ones. Despite having different touch-down and lift-off angles, the effective angular movement (about 40 °) is comparable between all species, except for Ochotona, which is more than 10 ° lower (Table 3B,C). The mean amplitude of the ‘pelvic movement’ during the stance phase is also lowest in Ochotona and highest in Procavia. At symmetrical gaits, two additional ‘pelvic movements’ occur. The first, a rotation about the dorsoventral axis, is caused by lateral additive intervertebral joint movements (‘lateral bending’; Jenkins and Camazine, 1977). The second is a rotation about the longitudinal axis (‘tilting’; Jenkins and Camazine, 1977). Because of the angle’s projection into the sagittal plane, estimates of lateral bending and tilting are difficult and were not attempted here. Sagittal spine movements result in a low mean EAD of 3 ° and a mean amplitude of 12 ° for all species at symmetrical gaits. The pelvis is held virtually stable during locomotion (Fig. 3A). Pelvic position is inclined the most in Procavia (51 ° at touchdown and 47 ° at lift-off) and more horizontal in Tupaia and Galea (19 ° to 16 °, and 22 ° to 19 °). Mean pelvic angles of all other species are in the order of 35 ° at touch-down and 32 ° at lift-off. Hindlimb Kinematics of hindlimb segments As in the forelimb, retraction of all hindlimb segments starts before touch-down in the last third of the swing phase at symmetrical and in-phase gaits. In particular ‘pelvic retraction’ at in-phase gaits also starts at the beginning of the stance phase and continues until the first quarter of the swing phase in trailing and leading limbs of all species (but only the leading limb of Procavia). Femoral retraction at symmetrical gaits ends after 95 % of the stance duration (Microcebus), at lift-off (Tupaia, Rattus, Procavia) or during the first 10 % of the swing phase (Monodelphis, Dasyuroides) (Fig. 3A). At in-phase gaits, femoral retraction is finished at lift-off or during the first 15 % of the swing phase in trailing and leading limbs of all species. Only in Ochotona, does retraction of the thigh start before lift-off. In all species, protraction of the lower leg begins during the first 35 % of the swing phase in both trailing and leading limbs; in Procavia, however, it begins in the late stance phase. At symmetrical gaits, lower leg retraction ends between 20–40 % of the swing phase in all species. Although retraction of the foot comes to an end in the first third of the swing phase in trailing and leading limbs of most species, but ends at the lift-off in Procavia and in the late stance phase in the trailing limb of Ochotona. Foot protraction starts in the first third of swing phase in all species at symmetrical gaits. Protraction and retraction of the hindlimb is executed mainly by femoral displacements at symmetrical gaits but by sagittal spine movements at in-phase gaits. At touch-down, the thigh is in an almost horizontal position in all species and at all gaits (7 ° at symmetrical gaits, –2 ° in trailing limb and –6 ° in leading limb at in-phase gaits). In species for which we have data for symmetrical and in-phase gaits, mean touch- 1328 M. S. Fischer and others A Hindlimb, walk Lift-off 70 Pelvis 60 Monodelphis domestica 50 Dasyuroides byrnei 40 Procavia capensis Galea musteloides 30 Rattus norvegicus 20 Tupaia glis 10 Microcebus murinus 0 140 120 Hip joint 140 100 120 80 100 60 80 40 Angle (degrees) Lift-off 160 Thigh 60 20 40 0 –20 120 20 140 Lower leg 100 80 60 120 40 80 Knee joint 100 20 60 0 –20 –40 160 140 120 100 80 60 40 20 0 –20 40 20 160 Foot Ankle joint 140 120 100 80 60 40 0 20 40 60 Step duration (%) 80 100 20 0 20 40 60 Step duration (%) 80 100 Fig. 3. Mean values of hindlimb segment angular excursions of typical sequences at symmetrical (A) and for trailing (B) and leading (C) limbs at in-phase gaits (see Fig. 2). down angles at in-phase gaits decrease to positions inclined above the horizontal. Fig. 4 illustrates the highly uniform thigh position that occurs, particularly at in-phase gaits. In comparison to touch-down, mean lift-off angles are more variable ranging from 51 ° in Dasyuroides and 125 ° in Tupaia at symmetrical gaits, as well as 47 ° and 101 ° in the trailing limb and 52 ° and 109 ° in the leading limb of Ochotona and Tupaia at in-phase gaits. The femoral retraction that follows ends with the maximum angle at liftoff or in the first part of the swing phase. Mean amplitudes of femoral displacement increase from symmetrical to inphase gaits in all species (except Tupaia) and are higher in the leading limbs than in the trailing limbs at in-phase gaits. The same mean amplitudes of both hindlimbs were only observed in Monodelphis at in-phase gaits, because animals performed half-bound gaits. Limb kinematics of small mammals 1329 B 90 80 70 60 50 40 30 20 10 0 –10 120 Hindlimb, in-phase, trailing limb Pelvis Lift-off Monodelphis domestica Dasyuroides byrnei Ochotona rufescens Procavia capensis Galea musteloides Tupaia glis Thigh 100 80 60 40 Angle (degrees) 20 0 –20 120 100 80 60 40 20 0 –20 –40 140 120 100 80 60 40 20 0 –20 Lower limb 120 110 100 90 80 70 60 50 40 30 Hip joint 140 Knee joint Lift-off 120 100 80 60 40 Foot 0 20 40 60 Step duration (%) 80 100 At symmetrical gaits, the lower leg is in almost vertical at touch-down in Microcebus, Procavia, Monodelphis and Rattus, but more caudally inclined in Dasyuroides, Tupaia and Galea (Fig. 4). From symmetrical gaits to in-phase gaits, mean touch-down angles increase in all species. At in-phase gaits, a nearly vertical position of the lower leg is realised in Monodelphis, Dasyuroides and Ochotona. Differences in this touch-down position were measured in Galea and Tupaia (which show a more posteriorly inclined lower leg) and in Procavia (in which the lower leg is more anteriorly directed in both trailing and leading limbs). In general, mean touch-down angles are comparable between trailing and leading limbs 20 140 130 120 110 100 90 80 70 60 50 40 Ankle joint 0 20 40 60 Step duration (%) 80 100 (Table 3B,C). The lower leg is retracted during the stance phase and reaches a horizontal orientation at lift-off (mean 1 ° at symmetrical gaits, 3 ° in trailing and 7 ° in leading limbs at in-phase gaits). In some species, the minimum angle of the lower leg is observed during the stance phase and afterwards the angle increases until lift-off by retraction of the foot at the end of stance. This biphasic motion of the shank (i.e. with two minima during one step cycle) is most pronounced in Tupaia at all gaits (Fig. 3A–C). Lower leg retraction reaches its maximum during the swing phase in all species at symmetrical gaits and in most species at in-phase gaits. Mean amplitudes are higher in all species at in-phase gaits than at symmetrical 1330 M. S. Fischer and others Angle (degrees) C 90 80 70 60 50 40 30 20 10 0 120 100 80 60 40 20 0 –20 –40 120 100 80 60 40 20 0 –20 –40 140 120 100 80 60 40 20 0 –20 Hindlimb, in-phase, leading limb Lift-off Pelvis Monodelphis domestica Dasyuroides byrnei Ochotona rufescens Procavia capensis Galea musteloides Tupaia glis Thigh Lower limb Foot 0 20 40 60 Step duration (%) 80 100 gaits, but are comparable in Monodelphis. Mean amplitudes of trailing and leading limbs are nearly the same in all species. The foot is in matched motion with the thigh, seen in particular during the stance phase at all gaits (Fig. 3A–C). Mean touch-down angles of all species occur over a small range of 4–19 ° at all gaits. As the foot is brought down, it is in a semidigitigrad position in all species, with the most erected foot seen in Procavia. The foot is in retraction and crosses its vertical position in all species during the stance phase at all gaits. Mean lift-off angle is variable at different gaits, ranging between 92 ° and 138 ° (Dasyuroides and Tupaia) at symmetrical gaits, 78–121 ° in trailing limbs and 81–126 ° in 120 110 100 90 80 70 60 50 40 30 120 110 100 90 80 70 60 50 40 30 140 130 120 110 100 90 80 70 60 50 40 Lift-off Hip joint Knee joint Ankle joint 0 20 40 60 Step duration (%) 80 100 leading limbs (Ochotona and Procavia) at in-phase gaits. Foot retraction is more restricted at in-phase gaits than at symmetrical gaits in all species (except Dasyuroides). After reaching its maximum retraction, the foot is protracted during the swing phase and the following retraction starts just before the next touch-down. Mean amplitudes of all species are highest at symmetrical gaits (104 °), slightly lower in the leading limb (101 °), and lowest in the trailing limb at in-phase gaits (99 °). Contribution of hindlimb segment movements to step length Whereas the femur is the most propulsive segment at Limb kinematics of small mammals 1331 Forelimb Touch-down Hindlimb Lift-off Touch-down Lift-off Symmetrical gaits Trailing limb In-phase gaits Monodelphis domestica Dasyuroides byrnei Ochotona rufescens Procavia capensis Galea musteloides Rattus norvegicus Tupaia glis Microcebus murinus Leading limb Fig. 4. Mean joint angles at touch-down and lift-off, illustrated as schematic fore- and hindlimb configurations considering limb proportions of all species under study (see Table 4) at symmetrical and in-phase gaits. Note the high uniform limb position at touch-down in contrast to that at lift-off and the more variable lift-off configuration of hindlimbs in comparison to forelimbs. symmetrical gaits with a mean contribution of 76 % to step length in all species, ‘pelvic movements’ contribute to half of the step length at in-phase gaits (Table 3A–C). At symmetrical gaits, the contribution of ‘pelvic movements’ is in the same low order as amplitudes for all species ranging between –3 % and 7 %. The highest value was found in Microcebus (10 %). At in-phase gaits, the contribution of ‘pelvic movement’ to step length is similar in all species because the same effective angular displacement of the pelvis occurs in species with and without tails. Values are also comparable for trailing and leading limbs in most species. The only differences observed were in Galea and Ochotona, where the contribution of ‘pelvic movements’ to trailing limbs is higher than to the leading limbs in Galea and the reverse is true for Ochotona (Table 3B,C). Displacement of the thigh at in-phase gaits contributes to about one third of the step length, but these data are highly variable between different species. The lowest values for contribution of thigh displacement to body forward movement were found in Ochotona (which also showed the lowest EAD) with only 8 % in the trailing and 10 % in the leading limbs. The highest values of EAD, which resulted in higher contributions to step length, were observed in Tupaia (46 % in trailing limbs and 53 % in leading limbs). Comparable values were calculated for more distal segments for hindlimbs at symmetrical gaits and for trailing and leading limbs at in-phase gaits. In general, the foot contributes more to step length (18 % at symmetrical gaits and about 12 % at in-phase gaits) than the shank (3 % at symmetrical gaits, 9 % in trailing and 4 % in leading limb at in-phase gaits). The reverse case, in which the contribution of shank movements exceeds the contribution of foot movements was found only for Ochotona and Procavia at in-phase gaits and for Procavia and Rattus at symmetrical gaits. Kinematics of hindlimb joints In general, flexion and extension of all hindlimb joints are more pronounced during symmetrical gaits than during inphase gaits (Fig. 3A–C). Comparisons of the limb joint behaviour of all species at in-phase gaits point to Ochotona as the species with the most restricted angular excursions and to Tupaia as the species with most extensive angular excursions. A biphasic angular movement, including one flexion and one extension per each stance and each swing phase, was found for knee and ankle joints in all species at all gaits. In contrast, hip joints show a monophasic behaviour at symmetrical and inphase gaits, meaning that extension enters into a short plateau during the first 20 % of stance at in-phase gaits (with the exception of Tupaia). At symmetrical gaits, the extension of the hip joint starts shortly before touch-down (80–95 % of duration of the previous step cycle). There, it lasts until 90 % of the stance phase in Microcebus and Tupaia, until 10 % of 1332 M. S. Fischer and others the swing phase in Monodelphis and until lift-off in all other species. At in-phase gaits, extension reaches its maximum before lift-off of the trailing limb of Procavia and Ochotona, at lift-off in Dasyuroides and after lift-off in all other species. Maximum angular extension of the hip joint in leading limbs occurs after lift-off in all species, but ends at lift-off in Ochotona. The knee flexes before touch-down in all species at all gaits and reaches its maximum flexion at mid-stance when the foot passes underneath the hip joint. Knee joint extension, however, starts at different times at the end of stance. Knee joint extension ends independently from gaits in only two species; at lift-off in Dasyuroides and after lift-off in Monodelphis. Knee joint flexion at symmetrical gaits starts before lift-off in Rattus and Microcebus and at lift-off in Tupaia, Galea, and Procavia. At in-phase gaits, extension ends at lift-off in trailing and leading limbs of Galea and after lift-off in Tupaia and Procavia. In Ochotona, knee joint flexion starts earlier in trailing than in leading limbs. The stance phase extension of the ankle joint continues into the subsequent swing phase in all species at symmetrical gaits. In most of the species, no major changes in timing were observed during the change from symmetrical to in-phase gaits. In Ochotona, in which only in-phase gaits were analysed, flexion starts before lift-off in trailing and in leading limbs. The highest CSP has the hip joint in all species indicating a high degree of horizontal versus vertical action (Table 3A–C). Values within species are higher at symmetrical gaits than at in-phase gaits. With a mean touch-down angle of 40 ° in all species, the hip joint is flexed more at symmetrical gaits than at in-phase gaits (56 ° in trailing and 50 ° in leading limbs). Whereas hip joint angles at touch-down are similar in trailing and leading limbs of Monodelphis and Dasyuroides, they are higher in the trailing than in the leading limbs in all other species. The range of mean touch-down angles for all species at inphase gaits is twice that of symmetrical gaits, but is higher at symmetrical gaits than at in-phase gaits for mean lift-off hip joint angle. The lowest mean value of the hip joint at lift-off was found in Dasyuroides (73–80 °) and the highest value in Tupaia (110–141 °) at all gaits. Mean (±S.D.; lift-off angles of all species under study are 111±21 ° at symmetrical gaits, 96±11 ° in the trailing limb and 100±11 ° in the leading limb at in-phase gaits. At lift-off, the hip joint of the leading limb is extended more than that of the trailing limb in Dasyuroides, Galea and Procavia and is nearly the same in both hindlimbs in the other species. Mean lift-off angle decreases with the change from symmetrical to in-phase gaits in most species, but is comparable between both gaits in Procavia and lower at symmetrical than at in-phase gaits in Dasyuroides. Owing to the higher values at touch-down and lower values at lift-off for in-phase gaits compared to symmetrical gaits, EAD is reduced at in-phase gaits. Mean maximum angular movement amounts to 75 ° at symmetrical gaits, to 45 ° in trailing limbs and to 54 ° in leading limbs at in-phase gaits in all species. The highest overall amplitudes were observed in Tupaia (110 °) at symmetrical gaits and the lowest in the trailing limb of Ochotona at in-phase gaits (26 °). Discussion Limb configuration at touch-down The uniform forelimb configuration at touch-down is characterised by a highly consistent scapular orientation at approximately the same angle at all gaits (in all species 41±5 ° at symmetrical gaits, 47±4 ° at in-phase, mean ± S.D.). At touch-down the relative height of the scapular pivot is equal during symmetrical gaits but spreads more widely at in-phase gaits. This reflects different elevations of the trunk. In addition, the forearm (which is in matched motion with the scapula), has a rather low range of touch-down angles. The elbow joint approximates a rectangular configuration at symmetrical gaits (86±8 °), but is more extended at in-phase gaits (94±10 °). The wider range of the shoulder joint and the humeral position (S.D. of both 14–17 °) is mainly due to the stronger extension in Tupaia and Microcebus, and stronger flexion in Dasyuroides. Together with the relatively longer forearm, which contributes to the overall limb length (Table 4), this leads to the most anterior touch-down position in Tupaia and Microcebus (Fig. 4). The touch-down position of Dasyuroides is within the range of the other mammals despite the stronger shoulder joint flexion. Within each species, the touch-down point is at a constant distance from the perpendicular of the scapular pivot, just below the eye. Increases in step length are due to a more posterior transition of the lift-off point. Observations on forelimb movement of the walking Didelphis marsupialis (Jenkins and Weijs, 1979) correspond to those of our small mammals. In Didelphis, scapular angle at touch-down ranges between 40–50 ° and the humerus is oriented almost vertically. Shoulder and elbow joints are extended approximately 130 ° and 110 °. The touch-down position of the forelimb in Cavia porcellus (Rocha Barbosa et al., 1996) is very similar to that of its near relative Galea at all gaits. In the case of exploratory walking in Rattus norvegicus (Jenkins, 1974b), overall forelimb excursions are reduced and the point of touch-down lies slightly ahead of a point directly beneath the shoulder joint. In this case scapular touch-down angle is higher (50–60 °) and humeral angle is smaller (45 °) in exploratory walking compared to moderate walking. Limb kinematics were documented cineradiographically for a series of small mammals by Jenkins (1971). Differences in humeral touch-down angles and positions of touch-down points between the species studied by Jenkins and our sample of small mammals are probably caused by the slow speed of the exploratory walk investigated by Jenkins. In Felis catus f. domestica, the forelimb is more extended at touch-down than in our animals. Whereas the scapular angle measured in cineradiographic studies is the same as in our species (40–46 °; Boczek-Funcke et al., 1996), shoulder and elbow joint angles are about 30 ° higher. Scapular touch-down angles obtained in Felis (using externally applied markers) amount to 40–50 ° (Miller and Van der Meché, 1975; English, Limb kinematics of small mammals 1333 Monodelphis Microcebus Monodelphis Microcebus Saguinus Saguinus Dasyuroides Dasyuroides Saimiri Eulemur Touch-down Ochotona Saimiri Lift-off Ochotona Eulemur Tupaia Galea Tupaia Galea Acomys Procavia Procavia Acomys Rattus Tragulus Rattus Forelimb Capra Capra Tragulus In-phase gaits Symmetrical gaits Monodelphis Microcebus Monodelphis Microcebus Saguinus Dasyuroides Saguinus Dasyuroides Saimiri Lift-off Touch-down Ochotona Ochotona Saimiri Eulemur Eulemur Galea Galea Tupaia Tupaia Rattus Rattus Acomys Procavia Hindlimb Acomys Procavia Fig. 5. Schemes of limb configurations at touch-down and lift-off in 14 species at symmetrical (grey) and in-phase gaits (black). Limb proportions are set into the same ratios to emphasize the overall kinematic pattern. 1978; Halbertsma, 1983). In primates, forelimb posture at touch-down is characterised by an increasing amount of extension in the shoulder and elbow joints, which together with proportional changes between forelimb segments, results in a cranial displacement of the touch-down point (Jouffroy et al., 1983; Larson et al., 2000; Schmidt and Fischer, 2000). With increasing body size in arboreal-quadrupedal primates the forelimb protraction augments (Schmidt and Voges, 2001). Cineradiographic studies of shoulder movements in primates indicate that the amount of scapular rotation is reduced in larger species by both a higher touch-down angle (57 ° in Cercopithecus aethiops: Whitehead and Larson, 1994; 49 ° in 1334 M. S. Fischer and others Eulemur fulvus: Schmidt and Fischer, 2000) and a lower liftoff angle. Only Capra hircus, the domestic goat, deviates clearly from other mammals in having a more extended limb, with shoulder joint angles of more than 135 ° and elbow joint angles of 120 ° (Lilje and Fischer, 2001). Scapular retraction starts at an angle of 61 ° in Capra and 56 ° in Tragulus javanicus (the mouse deer; unpublished data) (Fig. 5). Whereas the forelimbs show no fundamental geometrical differences between symmetrical gaits and in-phase gaits, in that three segments are always displaced, hindlimb protraction is also executed by three hindlimb segments at symmetrical gaits. At in-phase gaits, intervertebral lower spine movements (causing a sagittal ‘pelvic displacement’) act functionally as an additional fourth segment. Despite this, femoral position is comparable at all gaits being almost horizontal at touch-down (in all species = 7±10 ° at symmetrical gaits, –2±5 ° in trailing limbs and –6±5 ° in leading limbs at in-phase gaits; means ± S.D.). This position is achieved by hip joint movement at symmetrical gaits, but is mainly passively induced by sagittal spine flexion (and to a lesser degree to hip joint flexion) at inphase gaits. As occurs in the forelimb, the distal segment is in matched motion with the femur. The foot is in the same position (S.D. ≤5 °) 12 ° at symmetrical gaits, 10 ° in trailing limbs and 9 ° in leading limbs at in-phase gaits. At symmetrical gaits, hip joints of all species have relatively similar positions at touch-down, indicated by a relative low value of S.D. (40±5 °). The knee joint, however, shows a little more variation (75±12 °) and the ankle joint is the most variable (80±20 °). Standard deviations increase in hip joints (56±12 ° in trailing limbs and 50±10 ° in leading limbs) whereas they are nearly constant, or decrease, in knee joints (77±11 ° resp. 75±6 °) and ankle joints (89±16 ° resp. 87±14 °) at in-phase gaits. Quantitative data on sagittal pelvic displacement are available for Cavia at trot and gallop (Rocha Barbosa et al., 1996). Its touch-down angle of 28 ° is similar to Galea and the two metatherians at symmetrical gaits. The high value of 70 ° at gallop corresponds to the data of tailless species in our sample. Gasc (1993) described hindlimb kinematics in the tailed rodent Meriones shawi at gallop. Although pelvic displacement was not quantified, angles at touch-down and liftoff can be estimated from a stick-figure drawing. Touch-down angles in Meriones are approximately 34 ° for trailing linbs and 32 ° for leading limbs and are always smaller than values measured in our tailed species. The pelvis touch-down angle of the walking Mephitis mephitis was also estimated from a stick-figure drawing (45 °; Van de Graaff et al., 1982) and lies in the range of our observations. Descriptions of hindlimb movements are available for a series of small to medium sized mammals. The touch-down position of the thigh in Didelphis, Tupaia, Mustela putoris (ferret), Mesocricetus auratus (hamster), Heterohyrax brucei (hyrax), and Rattus is more or less horizontal (Jenkins, 1971), and corresponds to angles reported here. The same is true for the Cavia (Rocha Barbosa et al., 1996) and for both trailing and leading limbs in the galloping Meriones (Gasc, 1993). As observed by Jenkins and Camazine (1977), the thigh is protracted at an angle of 30 ° below the horizontal line in Felis, Vulpes fulva (the fox) and Procyon lotor (the racoon) at touchdown. The highest mean touch-down angle of the thigh (51 °) is given for Mephitis by Van de Graaff et al. (1982). The more retracted thigh in Felis (Kuhtz-Buschbeck et al., 1994) and Mephitis reflects a more extended limb with higher extension of both hip joint (65 ° and 97 °, respectively, in comparison to our sample mean 43 °) and knee joint (120 ° and 154–73 °). The ankle joint angles are also more extended, being approximately 30 ° in Felis (Kuhtz-Buschbeck et al., 1994) and 60 ° in Mephitis (Van de Graaff et al., 1982). Limb configuration at lift-off Limb configuration of the forelimb at lift-off consists of a vertically placed scapula (in all species 92±7 ° at symmetrical gaits, 87±9 ° at in-phase; means ± S.D.) and a nearly horizontally placed humerus, especially at in-phase gaits (–13±7 ° respectively –2±9 °). The scapula initiates lift-off (Roberts, 1974), more or less waiting the last 20 % of the stance phase for the other joints to take off. The actual lifting off is caused by a strong flexion in the elbow. It is interesting to note that elbow extension decreases with increasing speed at walk and slow trot but increases with increasing speed at in-phase gaits (Fischer, 1998; Fischer and Lehmann, 1998; Schilling and Fischer, 1999; Schmidt and Fischer, 2000). The mean (±S.D.) lift-off angle of the pelvis (30±11 °) compared to that at touch-down (33±11 °) indicates that only minor ‘pelvic movements’ occur at symmetrical gaits. Lower mean values for pelvic lift-off position, in the leading compared to trailing limbs, is caused by the ongoing sagittal extension during stance (18±18 ° versus 21±18 °). In comparison to limb configuration at touch-down, hindlimb position at lift-off is more variable among all species, especially in the knee joint, caused by differences in retraction excursions of the thigh. Knee joint and thigh lift-off position are more variable between all species at symmetrical gaits (83±27 °, 81±26 °) than in trailing limbs (78±23 °, 75±23 °) and leading limbs (87±17 °, 82±22 °) at in-phase gaits. Hindlimb configuration at lift-off is marked by a horizontal positioning of the shank at all gaits (in all species = 1±11 ° at symmetrical gaits, 3±16 ° in trailing limbs and 7±14 ° in leading limbs at inphase gaits; means ± S.D.). The pelvis in Mephitis is in a more inclined position at touch-down and at lift-off at symmetrical gaits (38 °; Van de Graaff et al., 1982) indicating a more inclined position in general in comparison to data presented here (30 °). Effective angular movement of the pelvis is a little bit higher in Cavia (12 °; Rocha Barbosa et al., 1996) than in Galea (3 °), but the amplitude (10 °) is comparable. The more extended limb configuration in Felis and Mephitis at symmetrical gaits is also represented in lift-off positions of hindlimb joints. At mean lift-off angles in hip and knee joints of 130 ° in Felis (KuhtzBuschbeck et al., 1994) and of 163 ° and 149 °, respectively, in Mephitis (Van de Graaff et al., 1982), all of these values are clearly higher than those of the species we studied (111 °, 83 °). Ankle joint angles at lift-off augment with increasing speed in Limb kinematics of small mammals 1335 Felis (113–146 °; Kuhtz-Buschbeck et al., 1994) and are comparable at lower speeds (0.33–1.19 m s–1) to the mean angle we observed (115 °). In comparison, the ankle joint is more flexed at lift-off in Mephitis (i.e. 84 ° at 0.28 m s–1; Van de Graaff et al., 1982). At in-phase gaits, femoral retraction of the trailing limb in the species studied here (47–109 °) range between values for Meriones (60 °; Gasc, 1993) and Cavia (90 °; Rocha Barbosa et al., 1996). Values for Galea (mean 86 °) investigated here are comparable to those for Cavia (90 °; Rocha Barbosa et al., 1996) indicating a nearly vertical position. Overall, the more inclined pelvic position in Cavia at in-phase gaits (Rocha Barbosa et al., 1996), indicates that pelvic positioning is similar to other tailless species studied here, except Galea. However, amplitudes and effective angular movements are comparable between both caviids. As in our tailed species, the pelvis is also oriented very near to the horizontal at liftoff in Meriones (6 ° for trailing and 9 ° for leading limbs; Gasc, 1993). The hip joint in the trailing limb is flexed most at lift-off in Meriones (65 °, Gasc; 1993), extended a little bit more in the species included in our study (mean 96 °, range 93–112 °) and extended most in Cavia (115 °; Rocha Barbosa et al., 1996). As in the hip joint, the knee joint is also flexed more in Meriones (51 °; Gasc, 1993) than in our species (59–119 °) or in Cavia (100 °; Rocha Barbosa et al., 1996). As far as the ankle joint is concerned, values for both Meriones (119 °; Gasc, 1993) and Cavia (107 °; Rocha Barbosa et al., 1996) are well within the range of values reported here (91 ° to 125 °). Amplitudes during stance phase Differences between symmetrical and in-phase gaits, observed in all joints, point to more elevated limbs in the latter gaits (Fig. 5, Tables 2A,B, 3A–C). As the extended position is held throughout the stance and flexion reduced, especially at midstance, all amplitudes of limb joints decrease during the transition from symmetrical to in-phase gaits in all species we studied. Scapular amplitudes range between 44 ° (Dasyuroides) and 60 ° (Galea and Rattus) during the stance phase at symmetrical gaits. These amplitudes are reduced at in-phase gaits, ranging from 37 ° to 48 °. Previously published values on scapular rotation in walking Rattus collected from cineradiography are lower than those measured here by approximately 15 ° (Jenkins, 1974b, but see our earlier remarks on slow exploratory walk). In Didelphis, scapular rotation amounts to 40 ° at a slow walk or to 50 ° at a fast walk (Jenkins and Weijs, 1979). The amplitudes of scapular rotation in Cavia deviate from those of our species by having higher values at both symmetrical (trot: 62 °) and in-phase gaits (gallop: 70 °), caused mainly by an extraordinary high angle at lift-off (107–115 °). Scapular amplitudes range from 38 ° (walk) to 42 ° (trot and gallop) in Felis (English, 1978b). Whereas the values for the walking Felis have been confirmed by a later cineradiographic study (40 °; see Boczek-Funcke et al., 1996), scapular rotation is underestimated in trotting Felis (58 °; Sontag and Cremer, 1978), most probably due to the external registration techniques of English’s study. Published data on shoulder joint amplitudes are in accordance with our observations. While maximum amplitudes during stance are relatively low in Felis (24–28 °; BoczekFuncke et al., 1996), observations in Didelphis (35–45 °; Jenkins and Weijs, 1979) and Cavia (46 ° at symmetrical and 35 ° at in-phase gaits; Rocha Barbosa et al., 1996) are close to ours. The amplitudes of elbow joint excursions during the stance phase in Felis (41 °), Didelphis (40 °) and Cavia (42 °) at symmetrical gaits, lie within the same small range as in the species analysed in this study. The digitigrad Felis resembles the digitigrad Procavia in overall behaviour of the wrist joint (Caliebe et al., 1991; Miller and Van der Meché, 1975) inasmuch as amplitudes are relatively low, especially with increasing speed and dorsiflexion is restricted. Amplitudes of ‘pelvic movements’ are highly comparable between all species under study indicated by low standard deviations at symmetrical (3 °) and at in-phase gaits (8 ° in trailing and 5 ° in leading limbs). The mean amplitude of ‘pelvic movements’ for all species in the current study is 12 ° at symmetrical gaits, the same as reported for Cavia (Rocha Barbosa et al., 1996). At in-phase gaits, the mean amplitudes of ‘pelvic movements’ range between 27 ° and 49 ° in trailing limbs and between 31 ° and 46 ° in leading limbs. The value for the trailing limb in Cavia is within the range given here (48 °; Rocha Barbosa et al., 1996) and is only a little bit higher than the mean value observed for Galea (44 °). The amplitude of thigh movements in the species studied here (during the stance phase at symmetrical gaits) ranges between 51 ° (Dasyuroides) and 84 ° (Monodelphis) in most species and is higher only in Tupaia (110 °). Values given by Jenkins and Camazine (1977) for Vulpes, Mephitis and Felis (63 °, 72 ° and 72 ° respectively) are in-between the range we observed. For in-phase gaits, data for femoral amplitudes at stance phase are only available for the trailing limb in Cavia (48 °; Rocha Barbosa et al., 1996) and for the leading limb in Meriones (70 °; Gasc, 1993). These values are comparable to those reported here, which range between 50 ° (Ochotona) and 98 ° (Monodelphis) in the trailing limbs and between 61 ° (Ochotona) and 109 ° (Tupaia) in the leading limbs. Whereas mean hip joint and knee joint amplitudes are comparable to each other at in-phase gaits (45 ° and 43 ° in trailing limbs and 54 ° and 44 ° in leading limbs), hip joint amplitude in the current study is twice as high as knee joint amplitude at symmetrical gaits (75 ° and 38 ° respectively). Hip and knee joint amplitudes are clearly different at all gaits in Cavia being 63 ° and 25 ° at trot and 63 ° and 35 ° in the trailing limb at inphase gaits (Rocha Barbosa et al., 1996). A remarkable decrease in the mean amplitude occurs in the ankle joint of Cavia during the change from symmetrical (80 °) to in-phase gaits (17 ° in trailing limb) (Rocha Barbosa et al., 1996). The mean amplitude of the trailing limb in Cavia falls short of the range observed here (35 ° in Ochotona and 74 ° in Monodelphis), but the value for ankle joint amplitude at 1336 M. S. Fischer and others symmetrical gaits is in between the range we found (36 ° in Microcebus and 88 ° in Tupaia). To summarize, kinematics accompanying the transition from symmetrical to in-phase gaits offer no uniform pattern as implied by earlier studies, which discussed reduced joint amplitudes at in-phase gaits compared to symmetrical gaits. Studies of the majority of limb joints in Procavia (Fischer, 1994) or of the shoulder joint in Cavia (Rocha Barbosa et al., 1996) suggested that angular movements at in-phase gaits were reduced, but there is no species-independent, single pattern that accompanies the transition from symmetrical to in-phase gaits. In the case of scapular movements and hip joint angular movements, amplitudes decreased in all of our species at inphase gaits. In Cavia, however, scapular displacements increased and hip joint angular movements remained constant (Rocha Barbosa et al., 1996). Whereas amplitudes decrease during the change from symmetrical to in-phase gaits in the shoulder joints of Procavia, Monodelphis, and Cavia (Rocha Barbosa et al., 1996), they increase in Galea and remain constant in Dasyuroides and Tupaia. Elbow joint excursions increase at in-phase gaits in Monodelphis and Galea and decrease in all other species. Wrist joint angular movements are more pronounced at symmetrical gaits than at in-phase gaits in Monodelphis, Dasyuroides and Tupaia. The reverse is true for Procavia, Galea, and Cavia (Rocha Barbosa et al., 1996). In the hindlimb, knee joint amplitudes decrease at inphase gaits only in Tupaia and increase in all other species, including Cavia (Rocha Barbosa et al., 1996), but are constant in Galea. Ankle joint amplitudes at in-phase gaits are only one quarter as high as at symmetrical gaits in Cavia (Rocha Barbosa et al., 1996). Although not as dramatic as in Cavia, decreases are also observed for ankle joint amplitudes in Galea and Tupaia, while increases were observed in all of the species we studied. Contribution of segments to step length The ‘overlay method’ approach (Fischer and Lehmann, 1998) that we used to calculate the contribution of displacements of different segments to step length, explicitly considers the vertical displacement of pivots during stance. As this is the first study that compares the segment’s contribution to step length, no other data outside our working group are available for comparison. Calculations indicate the predominance of scapular retraction in forelimb movement, while the contribution of humeral displacement to step length is always less than half of the scapular value. The contribution of the forearms only exceeds the value of the upper arm in species in which the forearm is extensively retracted, such as Tupaia at symmetrical gaits or Galea at in-phase gaits. Hand movements contribute to step length in most species with approximately 5 % and never more than 10 %. Despite the different limb configuration of artiodactyls and the lowest amplitudes of scapular rotation observed, the contribution to step length of the most proximal segment is the highest (73 %) in the goat, simply because of the high scapular pivot (Lilje and Fischer, 2001). Our calculations of the scapular contribution does not consider translation of the scapula along the thoracic wall known from the aclavicular Felis (BoczekFuncke et al., 1996) and Procavia (Fischer, 1998). The more extended limbs observed in most species at in-phase gaits lead to a more elevated position of the body and thus a higher scapular or elbow pivot. So the same or even higher contribution to step length can be achieved by lower effective angular movements (EADs). As in the forelimb, analysis of the contribution of segment’s movement to step length, point to the most proximal element as the most propulsive segment in the hindlimb. Because of the fundamental change in hindlimb motion between symmetrical and in-phase gaits, resulting in a different number of acting segments, distinct changes in the contributions of individual hindlimb segments occur. At symmetrical gaits, femoral protraction and retraction contribute three-quarters to step length and the remainder is mainly contributed by foot and shank movements. ‘Pelvic movements’ contribute only to a lesser degree. In contrast to this, the main part of body propulsion – half the step length – is contributed by additive sagittal spine movements at in-phase gaits. Despite the differences in touch-down and lift-off positions of the pelvis in tailed and tailless species, their contribution of ‘pelvic movements’ is comparable, owing to similar effective angular movements. One third of step length is added by thigh movement at in-phase gaits and the rest is shared by foot and shank movements. Final conclusion The comparison of kinematic data of different therian mammals suggests that therian mammals with small body sizes (90–2500 g) display the same overall behaviour of limb displacement during locomotion. To test this hypothesis, we included Procavia in our analysis, which descends most probably from larger cursorial ancestors and is secondarily dwarfed (Thenius, 1979; Fischer, 1986, 1992). Tragulus, the smallest ruminant, also supports the hypothesis that mainly body size constraints the kinematic pattern (Fig. 5). In general, kinematics of small therian mammals are obviously independent of their systematic position (at least in species selected here), of their natural habitat (when we accept that kinematics on the treadmill parallels unrestrained kinematics), and also of specific anatomical dispositions. Obviously, characters such as finger or toe reduction, fusion of zygpopodial elements, reduction of the clavicle, carpal or tarsal specializations, and even extreme elongation of metapodials in Tragulus do not affect the overall kinematic pattern of therians. The consequences of gait change from symmetrical to inphase gaits are strikingly different on forelimb and hindlimb. Whereas only timing changes on the forelimb (kinematics remain the same!), hindlimb kinematics change significantly. In small therian mammals, in-phase gaits are marked by an extensive sagittal bending of the lumbar spine as has been shown by cineradiography. Small intervertebral movements add up and pelvic retro- and protraction is their obvious effect (Fischer, 1994; Rocha Barbosa et al., 1996; Schilling and Limb kinematics of small mammals 1337 Fischer, 1999). Sagittal spine movements contribute roughly one half to the total propulsive movement during stance at inphase gaits. The occurrence or absence of a long tail influences the pelvic position at touch-down and lift-off but not the total displacement. The pelvic course of movement starts from a nearly vertical position in tailless species and at a more caudally inclined position in tailed species. It ends at a horizontal position in tailed species at lift-off and a more inclined position in tailless species (Fig. 4). We have problems interpreting the graph of the tailless Galea since it behaves more like a tailed species. For example, observations on Cavia (Rocha Barbosa et al., 1996), a sister taxon of Galea, show the typical pelvic course of movements as in our tailless species. Studies on midsize carnivores (Felis, Vulpes, Procyon) and our data on Capra strongly suggest that the elevated limb position of these forms has some influence on their kinematics. Still, the three-segmented fore- and hindlimbs are displaced in the same proximal pivots as in the smaller therians, and these are situated at the same level. While the scapular displacement remains the same in Felis, scapular EAD is reduced in Capra. In contrast, the high location of the scapular pivot leads to the highest contribution to step length in this artiodactyle. As a consequence of the more extended limbs, the position of humerus, femur and shank is more inclined at the beginning and end of stance with respect to their horizontal position in small therians. As there are no cineradiographic data on midsize or even larger mammals at in-phase gaits, we cannot estimate the impact of gait change on kinematics and especially on lower spine movements. The identification of a basically uniform pattern of kinematics in small therians leads to the suggestion, that mesozoic mammals of the therian stem lineage, which have been small to very small (Jenkins and Schaff, 1988; Krebs, 1991; Hu et al., 1997; Ji et al., 1999; Luo et al., 2001) had the same kinematic pattern. This configuration of limb segments is considered to represent the ancestral therian design of limbs with respect to other amniotes and especially monotremes (Pridmore, 1985). Its main function can be seen as an adaptation to irregularities of the ground. Such irregularities are thought to pose major handicaps for therians with parasagittal placed limbs (Fischer, 2001). Relative to small body sizes, support on ground or on off-ground strata are comparable, as has already been pointed out for Tupaia by Jenkins (1974a). Therefore, discussion on arboreality in small mammals seems inadequate. In summary, basic elements of locomotion of small to midsize therians are: (1) a three-segmented limb with zigzag configuration, which is mainly displaced at the highest possible pivot; (2) position of scapular pivot and hip joint at the same height over the ground at symmetrical gaits and consecutively similar functional length of fore- and hindlimbs; the matched motion of two segments (scapula/lower arm, femur/metatarsus) during retraction of limbs; (3) kinematics of forelimbs are independent of speed and gait; (4) the fundamental change from femur retraction at symmetrical gaits to sagittal spine movement at in-phase gaits resulting in different hindlimb kinematics; (5) propulsive movement of the body is mainly achieved by the most proximal acting limb segments (scapula and femur at symmetrical gaits, scapula and sagittal spine movements at inphase gaits) while all further distal limb joints contribute only to a lesser degree to step length. 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