Function generation synthesis of planar 5R mechanism

Abstract

This paper deals with the function generation problem for a planar five-bar mechanism. The inputs to the mechanism are selected as one of the fixed joints and the mid-joint, whereas the remaining fixed joint represents the output. Synthesis problem of the five-bar mechanism is analytically formulated and an objective function is expressed in polynomial form. Function generation synthesis is performed with equal spacing and Chebyshev approximation method. The four unknown construction parameters and the error are evaluated by means of five design points and the coefficients of the objective function are determined by numerical iteration using four stationary and one moving design point. Stationary points are placed at the boundaries of the motion and the moving point is re-selected at each iteration as the point corresponding to the extremum error. Iterations are repeated until the values are stabilized. The stabilization usually occurs at the third iteration. By this method, the maximum error values are approximately equated, hence the total error is bounded at certain limits. Finally the construction parameters of the mechanism are determined.