Graphical interpretation of the solution to the redundant problem in biomechanics

Chao, E. Y.<sup>1</sup>; An, K. N.<sup>1</sup>

Affiliations

¹Orthopedic Biomechanics Laboratory, Mayo Clinic/Mayo Foundation, Rochester, Minn. 55901

Abstract

Force analysis of musculoskeletal joint systems is a redundant problem since the number of unknowns exceeds the number of equilibrium and constraint equations. Such a problem has been analyzed previously by the method of permutation/combination and by optimization technique. This paper combines both methods and discusses the results in the light of a graphical presentation from which unique and nonunique solutions to the problem are elaborated. When the applied load is nominal, multiple solutions are possible to meet the functional requirements. However, under maximum strength, unique solution exists because the redundant muscles reach their physiological limits.

Links

DOI: 10.1115/1.3426207

WoS: A1978FL18500008

History

Received: 1978-03-08

Cited Works (2)

Year	Entry
1976	Chao EY, Opgrande JD, Axmear FE. Three-dimensional force analysis of finger joints in selected isometric hand functions. J Biomech. 1976;9(6):387-396.
1973	Seireg A, Arvikar RJ. A mathematical model for evaluation of forces in lower extremeties of the musculo-skeletal system. J Biomech. May 1973;6(3):313-326.

Cited By (18)

Year	Entry
1990	Yamaguchi GT. Performing whole-body simulations of gait with 3-D, dynamic musculoskeletal models. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:663-679.
1984	Dul J, Townsend MA, Shiavi R, Johnson GE. Muscular synergism, I: on criteria for load sharing between synergistic muscles. J Biomech. 1984;17(8):663-673.
1986	Brand RA, Pedersen DR, Friederich JA. The sensitivity of muscle force predictions to changes in physiologic cross-sectional area. J Biomech. 1986;19(8):589-596.
1988	Bean JC, Chaffin DB, Schultz AB. Biomechanical model calculation of muscle contraction forces: a double linear programming method. J Biomech. 1988;21(1):59-66.
1993	Kuo AD, Zajac FE. A biomechanical analysis of muscle strength as a limiting factor in standing posture. J Biomech. 1993;26(suppl 1):137-150.
1987	Pedersen DR, Brand RA, Cheng C, Arora JS. Direct comparison of muscle force predictions using linear and nonlinear programming. J Biomech Eng. August 1987;109(3):192-199.
2005	Chancey VC. Strength of the Human Neck: Understanding the Contributions of the Ligamentous and Muscular Spine in Tension and Bending [PhD thesis]. Duke University; 2005.
2001	Reffeor WS. Three Dimensional Dynamic Analysis of the Human Hand for Predicting Tendon, Ligament and Nerve Wear in the Carpal Tunnel During Typing [PhD thesis]. East Lansing, MI: Michigan State University; 2001.
1986	Buchanan TS. A Biomechanical Analysis of the Neural Control of Muscles about the Human Elbow Joint During Isometric Tasks [PhD thesis]. Evanston, IL: Northwestern University; June 1986.
2015	Wohlman SJ. Understanding the Dynamics of Thumb-Tip Force Generation Through Integration of Simulation and Experimental Methods [PhD thesis]. Evanston, IL: Northwestern University; August 2015.
1989	Yamaguchi GT. Feasibility and Conceptual Design of Functional Neuromuscular Stimulation Systems for the Restoration of Natural Gait to Paraplegics Based on Dynamic Musculoskeletal Models [PhD thesis]. Stanford University; August 1989.
1992	Kuo AD. Visualization Techniques for Analyzing Control of Human Movement: Affine Mappings Between Multidimensional Spaces [PhD thesis]. Stanford University; December 1992.
1997	Valero Cuevas FJ. Muscle Coordination of the Human Index Finger [PhD thesis]. Stanford University; April 1997.
1988	Son K. Biomechanical Analyses of Weight-Moving Tasks in the Seated Position [PhD thesis]. University of Michigan; 1988.
2012	Kurse MU. Inference of Computational Models of Tendon Networks Via Sparse Experimentation [PhD thesis]. University of Southern California (USC); August 2012.
2012	Raths C. Neuromuscular Dynamics in the Context of Motor Redundancy [PhD thesis]. University of Southern California (USC); August 2012.
2021	Marjaninejad A. Autonomous Learning for Robots in the Context of Brain-Body Interactions [PhD thesis]. University of Southern California (USC); August 2021.
1996	Choi H. Muscle Forces and Spinal Loads in the Human Neck: An EMG Experiment and a Comparison of Three Modeling Methods [PhD thesis]. University of Wisconsin – Madison; 1996.