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The matrix method of linkage analysis is extended to the analysis of the bearing forces and torques which result from the inertia of the moving links when a single-loop, single-degree-of-freedom linkage is driven with known input velocity and acceleration. The method is well suited to digital computation and has been tested on several examples of spatial linkages, one of which is presented. A 4 × 4 “inertia matrix” is defined to describe the mass distributions of the links, and a matrix expression is derived for their kinetic energy. The dynamic bearing reactions are found by using the Lagrange equations with a varying constraint.
John J. Uicker (1967) studied this question.