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

In single-degree-of-freedom (DOF) mechanisms, velocity coeffi-cients (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 systematical-ly uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar linkages. The proposed algorithm is efficient enough to be the kin-ematic block of any dynamic model of these linkages; also, it lends itself to pre-sent planar kinematics in graduate and/or undergraduate courses.