Kinematic analysis of multi-DOF planar mechanisms via velocity-coefficient vectors and acceleration-coefficient Jacobians

In the literature, velocity coefficients (VCs) and acceleration coefficients (ACs) were substantially proposed for single-degree-of-freedom (single-DOF) planar mechanisms. Their effectiveness in solving the kinematic analysis of these mechanisms is due to the fact that they only depend on the mechanism configuration. Such property also holds when they are defined for spatial single-DOF scleronomic and holonomic mechanisms, but was not exploited; moreover, some extensions of the VC and AC concepts to multi-DOF planar (or spatial scleronomic and holonomic) mechanisms are possible, but have not proved their practical usefulness. Here, first, the velocity-coefficient vectors (VCVs) together with their Jacobians (acceleration-coefficient Jacobians (ACJs) are proposed as an extension of the concepts of VC and AC to multi-DOF scleronomic and holonomic mechanisms. Then, a general algorithm, based on VCVs and ACJs and on a notation, previously presented by the author, which uses the complex-number method, is proposed for solving the kinematic-analysis problems of multi-DOF planar mechanisms and to find their links’ dead-center positions. The effectiveness of the proposed algorithm is also illustrated by applying it to a case study. The proposed algorithm is efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, and simple enough for being presented in graduate courses.