Kinematic and dynamic analyses of cascades of planar four-bar mechanisms

Abstract

Computer programs have been developed for the kinematic and dynamic analyses of cascades of planar four-bar mechanisms. Since the analytic approach has high efficiency and accuracy in computation, a chain of four-bar linkages is developed horizontally and vertically by using the relative coordinates and the absolute coordinates, from which the explicit equations and the simultaneous equations are respectively derived in the kinematic analysis. In this analysis, the actions of transmission of linkages, from left to right, from right to left and from lower to upper, are performed by the image method and transformation procedures. Based on the kinematic analysis, the dynamic analysis is also developed by using both sets of coordinate systems. The generalized equation of motion, the general form of Lagrange's equations, Lagrange multipliers and the theorem of power balance are used to construct various formulations of the governing equations of motion for some particular problems. The problem of a linkage with a moving frame (the ground link) is the most interesting focus in this analysis.