The kinematics and vibration of planar linkage mechanisms

Abstract

This thesis reports an investigation into three problems encountered in the design of linkage mechanisms, namely kinematic synthesis, balancing of inertia forces and vibration analysis. A general method of synthesizing planar linkages with pin and sliding joints using an Optimization approach has been investigated. A concise but easily interpreted technique for prescribing the topology of linkages formed by connecting pairs of links together has been developed. The displacement analysis of a linkage is achieved using a direct method which is considerably faster than alternative techniques. A nonlinear optimization algorithm has been modified to cater for non-linear constraints such as transmission angle. These techniques have been incorporated into a computer program. Two case-studies of using the program are given. The first is the synthesis of a six-bar linkage for a motorcycle rear suspension such that a constant centre distance is maintained between the chain-wheels as the suspension deflects. The second concerns the modification of two linkages, containing eight and ten links respectively, to give an improved knitting action for a warp-knitting machine. Operating linkages at high speeds can result in rapidly varying forces acting on the frame due to the mass of the moving links. A procedure to determine suitable counterweights to balance these forces has been developed. Since adding the counterweights may double the total mass of the linkage, the links should have minimum mass. If the mass of a link is reduced too far, the link may vibrate and so detrimentally affect the performance of the linkage. Accordingly the final part reports an investigation into the forced vibration, assuming stability, of a 'Uniform, pin-jointed, binary link. The equations of motion are derived and stability boundaries determined. The theoretical predictions are compared with experimental results from the coupler of a four-bar linkage.