The role of the mass matrix in the analysis of mechanical systems

Abstract

This paper proposes a simple, intuitive method of analyzing and understanding the mass matrix of a mechanical system. With very little calculation, it is possible to determine four important values that describe the inertia and inertial coupling of a mechanism: the locked effective inertia, the force coupling, the free effective inertia, and the acceleration coupling. These values can be determined for a system formulated in terms of joint coordinates, but when used with systems formulated in terms of workspace coordinates, this work provides a unified method of determining important, well-established concepts such as effective mass (particularly important in the field of human-robot interaction) and dynamic isotropy (an important consideration for robotic manipulators and haptic devices). Two examples are provided which highlight the use of this method to analyze robotic manipulators.