# Are Torque-Driven Simulation Models of Human Movement Limited by an Assumption of Monoarticularity?
###### Abstract  
Subject-specific torque-driven computer simulation models employing single-joint torque generators have successfully simulated various sports movements with a key assumption that the maximal torque exerted at a joint is a function of the kinematics of that joint alone. This study investigates the effect on model accuracy of single-joint or two-joint torque generator representations within whole-body simulations of squat jumping and countermovement jumping. Two eight-segment forward dynamics subject-specific rigid body models with torque generators at five joints are constructed--the first model includes lower limb torques, calculated solely from single-joint torque generators, and the second model includes two-joint torque generators. Both models are used to produce matched simulations to a squat jump and a countermovement jump by varying activation timings to the torque generators in each model. The two-joint torque generator model of squat and countermovement jumps matched measured jump performances more closely (6% and 10% different, respectively) than the single-joint simulation model (10% and 24% different, respectively). Our results show that the two-joint model performed better for squat jumping and the upward phase of the countermovement jump by more closely matching faster joint velocities and achieving comparable amounts of lower limb joint extension. The submaximal descent phase of the countermovement jump was matched with similar accuracy by the two models (9% difference). In conclusion, a two-joint torque generator representation is likely to be more appropriate for simulating dynamic tasks requiring large joint torques and near-maximal joint velocities. computer simulation; joint torque; biparticular muscle 28 January 202120 April 202124 April  
or better when evaluating a variety of movements such as tumbling 1% [1], single-legged jumping 7-11% [8], vaulting 6% [4], triple jumping 2% [9] and springboard diving 4% [10]. One underlying assumption of torque-driven simulation models has been that the torque at any joint is a function of only that joint's kinematics [11]. This assumption of monoarticularity has been made throughout the literature [12; 13; 14]. Subject-specific torque-driven simulation models have assumed monoarticularity when representing the torques measured on a dynamometer which subsequently inform the strength of the model [3; 4]. Typically, this incorporates a representation of maximum voluntary torque at a joint as a function of the joint angle and joint velocity [15; 16]. This representation of joint torque is a simplification of the more complex summation of individual muscle forces which create a joint moment. It has long been established that the force generated by a muscle is a function of its length [17], and its velocity of shortening [18; 19] or lengthening [20]. For a biaarticular muscle, the length and velocity of the muscle are defined by the kinematics and moment arms of both the joints that it crosses. There is reason to suspect that a single-joint or monoarticular only assumption may under certain circumstances introduce doubt into the understanding of human movement obtained from torque-driven simulations. Firstly, it has been proposed that biariticality may enable greater work to be performed by the body than if it were composed of only monoarticular muscles [21; 22]. This is best illustrated by considering the effect of concurrent hip extension and knee extension on the length of the hamstring muscle group in activities such as jumping and running [11]. Hip extension imposes a shortening effect on a monoarticular muscle crossing posteriorly only the hip joint, whereas, for a biaarticular muscle such as the hamstring that also crosses the knee, knee extension introduces a lengthening effect (although not necessarily equivalent in magnitude, due to differences in the moment arms at the knee and hip).