Deflection and Stress Analysis in High Speed Planar Mechanisms With Elastic Links

In the design of high speed machinery the solution of the kinematics problem alone may in certain cases not be sufficient due to the elastic nature of the mechanism parameters. A method of deflection analysis, suitable for computer programming, is presented here which is general for all planar linkages including multi-loop mechanisms. This generality is accomplished by the extension of the permutation vector method of structural analysis to the kineto-elastodynamic analysis of mechanisms and by the introduction of the rate of change of the eigenvalues with respect to the motion of mechanisms. Both of these methods are believed to be applied here for the first time in the area of linkage design. With these methods an eigenvalue problem of high order is solved whereby the required computation time is decreased by a factor of three with respect to conventional numerical methods in most cases. Furthermore a method of dynamic stress analysis is presented to indicate the relationship between the dynamic stresses and the mechanism design parameters. Several numerical examples illustrate the concepts developed in this paper.