Systematic Use of Velocity and Acceleration Coefficients in the Kinematic Analysis of Single-DOF Planar Linkages

摘要

In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage, complex numbers are an easy-to-use tool for writing linkage's loop equations that are formally differentiable. Here, both these results are combined to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar linkages. The proposed algorithm is efficient enough to be the kinematic block of any dynamic model of these linkages; also, it lends itself to present planar kinematics in graduate and/or undergraduate courses.