Kinematic analysis of hinge-lever mechanisms with description of the motion in the Lagrange form

摘要

We propose a technique for the kinematic analysis of the hinge-lever mechanisms with the description of the motion in the Lagrange form, which makes it possible to use the explicit form of the mathematical description of the coordinates and the components of the velocities and the accelerations of any points that are specified by the initial coordinates, and also makes it possible to increase the accuracy of the calculations, including the calculations in the vicinity of the critical points (the cusp points). We present the relationships between the angular velocities and accelerations of the various members for the most widely used crank mechanism schemes. We present an example of the use of the technique for the Chebyshev mechanism. The technique leads to reduction of the difficulties in developing the computational programs, and has advantages in analyzing the linkage curves and in the subsequent dynamic analysis of mechanisms.