Biarticulate muscles—muscles that span more than one joint—are ubiquitous throughout the animal kingdom, suggesting that they have important evolutionary advantages.¹ Biomechanically, these muscles have been ascribed the function of transferring energy from proximal to distal lower limb segments and are believed to have an inverse role in shock absorbency.²However, robotic legs are generally designed using only one rotational motor at each joint, which introduces a number of problems when designing walking machines. First, most motors are not back-drivable (they cannot be turned easily when switched off). This means the motor must be powered at all times, even when the natural motion of the limb would only require that it swing freely and the joint rotate passively. Thus, though a robot might mimic a zero-energy trajectory, the process of mimicry requires energy. Second, in order to generate large forces needed at the ankle (during running, for instance) large motors may be needed. This places a large mass at the end of the leg, increasing its moment of inertia and so reducing overall efficiency. Traditional robotic leg designs are therefore impoverished models human legs.

By contrast with conventional robot leg designs, the mammalian leg works on very different principles: it can be modeled as a system of three planar joints (hip, knee, and ankle) and nine muscle actuators. Each joint is actuated by a combination of flexor and extensor muscles arranged in agonist/antagonist configuration. In this configuration, monoarticulate muscles (spanning one joint), are used to rotate the joint by pulling on the limb segments from either side. One muscle flexes the joint, while the other extends it. When neither muscle is active the joint can swing freely.

Shown above is a cut-away view of the robot leg. High performance modular motors pull on Kevlar straps to activate the joints. The biarticulate actuators are the gastrocnemius (GA) and rectus femoris. Hamstrings are not implemented here.

In addition to the monoarticular, many muscles in the human body are biarticular. That is, these muscles span two joints rather than one. Our leg model includes three biarticulate muscles: the gastrocnemius (GA), the rectus femoris (RF) and hamstring muscle group (HA). The gastrocnemius muscle attaches to the femur and the back of the heel, thus acting on both knee and ankle joints. If the GA is activated then the ankle is forced to rotate as the knee rotates, allowing the muscles acting on the knee to do work on the ankle. The knee is extended by muscles including the rectus femoris (RF), itself a biarticulate muscle anchored to both the hip and knee and the vatus lateralis (VA) acting on both the femur and knee. Finally, the gluteus maximus (GLM), assists in extending the femur. The above effects lead to chain of energy transfer:

This configuration was used to measure the contribution of the soleus (SO) and GA to the ankle power as well as to analyze the effect of the SO and GA activation timing on peak power production.

Shown is the power versus time at ankle during the return from a squat: (A) SO alone, (B) GA alone (C) SO and GA.

To test the idea of energy transfer, and to better understand the coordination of mono and biarticulate muscles, we implemented these ideas in a human-like leg (Figure 1). We will call the complete robot with legs and a torso Achilles. Each joint is actuated by a combination of actuators designed to mimic the mechanics of the leg. The following muscles were modeled: GA, TA (tibialis anterior), SO (soleus), VA, RF, GLM and IL (illiacus). The HA and BFS (bicep femoris) are not modeled here. The distances and proportions of the limb segments are based on human anthropometric data.³

In our experiments, we commanded the leg to lift itself from a squat to standing on its toes (Figure 2), while measuring force exerted at the heel and in the soleus and gastrocnemius. Using this data, we were able to compute the work done at the heel when either or both muscles were activated. Our results show the effect of power transfer from the knee to the ankle when the gastrocnemius is active (Figure 3).

We also found that a slight delay between activation of the GA and SO optimized power transfer at the ankle. This is consistent with measurements of muscle activation in humans.^3,4

These results show that, in practice, it is possible to use biarticulate muscle activation to transfer power between joints, which could significantly improve power efficiency in walking machines. In addition, these results hold out the possibility of using biarticulate muscles to absorb energy in landing, by transferring energy from force on the ankle into work on the knee and hip. Our intent is to incorporate this leg into a bipedal humanoid robot. Currently, we are working on an improved version of the leg that will model the BFS and hamstrings, allowing for walking and possibly running and stair climbing. When competed, this biped will be a unique contribution to the design of humanoid and walking robots. Further details are available in our paper.⁵

2. B. I. Prilutsky and V. M. Zatsiorsky, Optimization-Based Models of Muscle Coordination, Exercise and Sport Sci. Rev. 1, pp. 32-8, 2002.
   
   
3. B. I. Prilutsky and V. M. Zatsiorsky, Tendon Action of Two-Joint Muscles: Transfer of Mechanical Energy Between Joints during Jumping, Landing, and Running, J. Biomech. 27, pp. 25-34, 1994.
   
   
4. D. A. Winter, Biomechanics and Motor Control of Human Movement, John Wiley & Sons, Inc., New York, 1990.
   
   
5. Y. Ivanenko, R. Poppele and F. Lacquaniti, Five basic muscle activation patterns account for muscle activity during human locomotion, J. Physiol. 87, pp. 3, 2004.
   
   
6. M. Anthony Lewis, Theresa J. Klein and Tuan Pham, On the design of walking machines using Biarticulate Actuators, 11^th Int'l Conf. on Walking and Climbing Machines, 2008.