On the dynamic equivalence of planar mechanisms, an inertia decomposition method

Abstract

In this paper the dynamic equivalence of planar mechanisms is investigated by decomposition of inertia into point masses. For a planar rigid body, two point masses can fully describe its dynamic behavior. The location of one these points can be chosen freely, fixing the second point. By locating one of the two point masses of a link on a revolute joint, this link can be fully described by the one remaining point mass. By applying this approach throughout the mechanism’s chain, a reduced parameterization of the dynamics is found. The inverse process— inertia recomposition—gives a range of dynamic equivalent mechanisms. This paper gives the bounds for the selection of such equivalent mechanisms. Simulations of two dynamically equivalent 4-bar mechanisms, derived using this method, show equal base reaction forces and moments, confirming the dynamic equivalence.