Closed loop problems in biomechanics. Part I--a classification system.

Abstract

Biomechanics researchers have relied heavily on the inverse dynamics approach for calculating the forces and torques at human joints. However, implicit in this approach is the assumption that there are sufficient independent equations of motion to uniquely determine these unknown kinetics. There exists a class of problems, commonly referred to as closed loop problems, when there are insufficient equations and indeterminacy arises. The purposes of the present paper are (1) to develop a general classification system of closed loop problems for whole body movements; and (2) to identify the minimum number of force transducing devices necessary to uniquely determine joint kinetics for these problems. The classification system is based on the human subject's interaction with his environment and with himself. Two criteria are considered: first, the number of the subject's extremities in contact with fixed external reference systems, and second, the number of closed loops formed by those extremities not in contact with fixed external systems. Different combinations of these two criteria are examined and grouped into five cases according to the degree to which the equations of motion are over-determined, determined, or under-determined. Examples are given to illustrate the concepts. It is felt that the use of this system should aid in the understanding of joint force and torque calculations, especially with regard to the under-determined cases.