Kinematics of the eccentric RPRPR chain with applications to robotics, materials handling and manipulation

Abstract

Two formulations of the RPRPR-chain kinematics are discussed, one using equations of constraint, the other a vector loop approach. These are compared with respect to motion-transmission indicators, differences in plotting the kinematic chain when assembly is not possible, and CPU time required by one set of calculations. By locking one or both sliding inputs of the RPRPR chain, the more commonly used RPRR oscillating slide and the RRR dyad are obtained, with offset points attached to moving links being modelled as triangular Baranov trusses. Simulations of numerous planar mechanisms can be performed using the equations presented. Examples given in the paper include rack-and-pinion four-bar and geared five-bar linkages, rope shovels, hydraulic excavators, 2D serial and parallel manipulators and leg mechanisms. The computer programs used to in these simulations allow for the automatic displaying of velocity and accelerations vectors of moving points, and of dynamics linear and angular dimensions or interest.