Procedures are presented for analyzing and designing planar mechanisms with elastic links and distributed mass, operating at prescribed input rotational speeds.

The set of governing equations for deflections about the rigid body trajectory of mechanism members is derived using the Lagrange equation. These equations are discretized by the finite element method. The equations derived in this thesis give a more refined mathematical model by including additional terms as compared to previous methods which represented mechanisms as a sequence of instantaneous structures. The element equations are transformed and assembled to generate the governing differential equations for the mechanism, using a connection procedure suitable for elements assumed axially rigid. Consequently a smaller set of global equations than those previously used is obtained.

A procedure is presented for finding the steady-state solution for these equations. The method involves representing the global matrices, the global load vector, as well as the mechanism deflections by truncated Fourier series. By matching harmonic terms, a system of linear equations is derived and solved for the harmonic deflection coefficients of the response.

Using the expansion of the global matrices into harmonic series, the problem of determining the critical running speeds, for a physically undamped mechanism, is reduced to that of an eigenvalue problem, and a discrete set of critical running speeds is found. A proposed method of determining the stable and unstable regions of input speed operation for a flexible mechanism is also presented.

A procedure for designing flexible mechanisms in a systematic manner is presented which involves proportioning link cross-sectional areas to ensure that the maximum stress in each link does not exceed a specified allowable limit throughout each cycle of motion. Iterations toward the optimum flexible mechanism design are made using a multi-dimensional gradient search. Gradients are calculated by considering stresses caused by external and inertia forces of the rigid body motions.