## Introduction

The structure of the human ankle and foot differs from that of apes and early hominins in many important respects (Lewis, 1980c; Stern & Susman, 1983; Latimer et al. 1987; Lovejoy et al. 2009; Zipfel et al. 2011), including the presence of longer plantarflexor (PF) moment arms and reduced joint mobility (Susman et al. 1984; Thorpe et al. 1999). These traits are among a suite of adaptations that allow the human foot to function as a rigid lever during bipedal walking (Bojsen-Møller, 1979; Susman, 1983), and as a compliant spring during running (Ker et al. 1987). Chimpanzees and other African apes, in contrast, appear to possess more mobile ankles and feet (Elftman & Manter, 1935a,b; Lewis, 1980a,b), which must therefore be capable of force generation over a wider range of leg and foot positions. However, to date, the effects of chimpanzee knee and ankle joint position on the three-dimensional moment-generating capabilities of the muscle–tendon units (MTUs) acting about the ankle and foot have not been fully investigated. Such data are essential for understanding the effect of skeletal morphology on MTU function, as well as for generating accurate estimates of muscle–tendon force and work output in dynamic analyses (Yamazaki et al. 1979; Thorpe et al. 2004; Sockol et al. 2007; Pontzer et al. 2009).

Moment arm length determines the amount of muscle force required to counter a given joint moment. The geometric definition of a moment arm is the perpendicular distance between the line of action of a MTU and the axis of rotation of the joint upon which the MTU acts. For a given MTU, this distance changes as a joint moves through its full range of motion. As a consequence, moment arm lengths often do not remain constant across joint positions. Two different methods have been devised to measure changes in moment arm length over a range of joint positions: the geometric-measurement method and the tendon-excursion method. For the geometric-measurement method, radiographic, computed tomography (CT), magnetic resonance or ultrasound images of a joint are collected at set intervals over a range of positions. The distance between the MTU line of action and an assumed joint center of rotation is then measured from each image (An et al. 1984; Rugg et al. 1990; Polk, 2002). The use of osteometrics to estimate moment arm lengths represents a simplified version of this method, and has been employed in many studies of locomotor or manipulative capabilities in living and fossil taxa (e.g. Schultz, 1963; Fleagle, 1976; Trinkaus, 1983; Strasser, 1992; Drapeau, 2004; Young, 2005; Raichlen et al. 2011). However, the accuracy of the geometric-measurement method is somewhat limited, because the MTU line of action and the joint center of rotation must be approximated (An et al. 1984; Spoor & van Leeuwen, 1992). In contrast, the tendon-excursion method involves the measurement of MTU excursion during angular motion at a joint. The derivative of the relationship between these variables provides instantaneous moment arm values across joint angles. This method follows the geometric law that when the radius of a circle rotates through one radian, the length of the arc traveled by any point on the radius will be equal to the distance between that point and the center of the circle. In the case of joint motion, to move a limb segment one radian, a tendon must be moved a distance equivalent to the perpendicular distance between the path of the tendon and the joint center of rotation. So, the derivative of the relationship between tendon excursion and joint angular excursion provides a measure of the true moment arm distance (Brand et al. 1975; An et al. 1983). Hence, no *a priori* knowledge of the MTU insertion or the joint center of rotation is needed.

Recent studies of ape moment arms have used the tendon-excursion method to document marked interspecific variation for many limb muscles, including those of the leg (Payne et al. 2006b; Channon et al. 2010). In the only such study of the common chimpanzee, Thorpe et al. (1999) measured the moment arms of the triceps surae muscles (i.e. m. gastrocnemius lateralis, m. gastrocnemius medialis and m. soleus) over the full range of PF–dorsiflexion (DF). However, these three MTUs have unique origins and, unlike in humans, chimpanzee gastrocnemius and soleus muscles maintain distinct bellies for most of the length of the leg (Swindler & Wood, 1973; Prejzner-Morawska & Urbanowicz, 1981). This raises the possibility that mm. gastrocnemius and m. soleus exhibit differences in their moment arm functions, especially for motion in non-sagittal planes. Further, Thorpe et al. (1999) did not consider the effect of knee position on the two-joint mm. gastrocnemius, nor did they collect data from any of the deep plantarflexors, peroneals or dorsiflexors. The main aim of this study, then, is to address this gap by evaluating the effect of joint position during motion in multiple planes on the force and moment-producing capabilities of all of the MTUs that cross the ankle in chimpanzees. Along with previous studies (Payne et al. 2006b; Channon et al. 2010), the data provided here will contribute to characterizing leg MTU moment arms across ape species. Additionally, this study involves direct measurements of chimpanzee ankle joint total ranges of motion, which is a topic of considerable interest (Stern & Susman, 1983; Latimer et al. 1987; DeSilva, 2009; Venkataraman et al. 2013), but for which little quantitative data are actually available from intact hind limbs.

The maximum moment-producing capabilities at the ankle are also dependent on the cross-sectional area of muscle that is available for force output. Muscle cross-sectional area is defined by its mass and architecture, including its average fascicle length and fascicle pennation angle (Alexander & Vernon, 1975; Lieber, 2010). As such, a second aim of this study is to provide new data on the architecture of the chimpanzee leg musculature. Muscle architecture data from the hind limbs of common chimpanzees (Thorpe et al. 1999; Nagano, 2001; Carlson, 2006; Myatt et al. 2011; Oishi et al. 2012) and other apes (Payne et al. 2006a; Channon et al. 2009) are still quite rare, and continued dissemination of new data is essential to elucidating intraspecific and interspecific variation as well as size-scaling patterns.