Tag Archives: tendon

hill type muscle model [1]

Hill Type Muscle Model with Matlab Code

Hill Type Muscle Model with Matlab Code

In this post, I will write on the Hill type muscle model, and then, I will provide a Matlab code made for the model. 

If you have a basic knowledge about the muscle tendon unit, and just want to download the Matlab code, just download from the following links

<Matlab m code> or <Matlab Simulink block>.

If you are familiar with Biomechanics, I think the best source to study a muscle tendon model is Zajac’s paper [4]. 

OK let’s go to the main writing.

Generally, the muscle tendon unit is modeled by the below figure including a CE (controctile component element), PE (parallel elastic element), and SE (series elastic element). This is the Hill type muscle-tendon model. The CE and PE are elements for a muscle, and the SE is for a tendon. Sometimes the SE is ignored in modeling, depending on tendon type, because its stiffness is very high.

hill type muscle model [1], Hill Type Muscle Model with Matlab Code

hill type muscle model [1]

The CE generates a contracting force on tendon, and the size of force is a function of the velocity/length of muscle as shown in the below equations. This is a general model, but sometimes the other model is used, depending on the type of muscle, if you want to know the detail refer [3]. 

Fce, Hill Type Muscle Model with Matlab Code

Force function of CE [2]

The PE element is modeled by the below equation. Again SE can be ignored, thus in my Matlab code, it is ignored.

Force of PE and SE, Hill Type Muscle Model with Matlab Code

Force of PE and SE [5]

Finally, we can make a model based on the above equations. In my code, I made a muscle-tendon model for finger muscles. If you want to model for the other muscle tendon unit, you have to search several parameters for the muscle.

You can download the Matlab code and Simulink code from below link. I made the same function with two different ways for user’s convenience.

<Matlab m code> or <Matlab Simulink block>.


E. M. Arnold, S. R. Ward, R. L. Lieber, and S. L. Delp, “A Model of the Lower Limb for Analysis of Human Movement,” Ann Biomed Eng, vol. 38, no. 2, pp. 269–279, Feb. 2010.
J. Rosen, M. B. Fuchs, and M. Arcan, “Performances of Hill-Type and Neural Network Muscle Models—Toward a Myosignal-Based Exoskeleton,” Computers and Biomedical Research, vol. 32, no. 5, pp. 415–439, Oct. 1999.
J. L. Sancho-Bru, A. Pérez-González, M. C. Mora, B. E. León, M. Vergara, J. L. Iserte, P. J. Rodríguez-Cervantes, and A. Morales, “Towards a realistic and self-contained biomechanical model of the hand,” 2011.
Z. Fe, “Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control.,” Crit Rev Biomed Eng, vol. 17, no. 4, pp. 359–411, Dec. 1988.
P.-H. Kuo and A. D. Deshpande, “Contribution of passive properties of muscle-tendon units to the metacarpophalangeal joint torque of the index finger,” in Biomedical Robotics and Biomechatronics (BioRob), 2010 3rd IEEE RAS and EMBS International Conference on, 2010, pp. 288–294.



I am Youngmok Yun, and writing about robotics theories and my research.

My main site is http://youngmok.com, and Korean ver. is  http://yunyoungmok.tistory.com.