A time finite element method is developed for the steady-state solutions of vibrating elastic mechanisms. The governing equations of motion for each individual link are described in a link (local) coordinate system with constant coefficients. The set of second order differential equations for all links are then coupled by a set of constitutive equations of elastic joint models describing the link interconnections. In utilizing time finite elements which discretize the forcing time period into a number of time intervals, the elastic motion is approximated by a set of temporal nodes of all spatial degrees of freedom of the mechanism system. The result is a set of linear algebraic system with a sparse structure and that can be solved effectively. A scotch york mechanism and a four-bar linkage are included as examples to illustrate the modeling and solution procedures applied.

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