Abstract

A formulation of the dynamical equations of a general, spatial, single-loop mechanism with any combination of rigid and flexible links is developed. This formulation resorts to the natural orthogonal complement (NOC) to eliminate non-working constraint forces from the equations of motion, an approach which offers several advantages. First, the equations of motion are formulated disregarding the non-working constraint forces, since they are eventually eliminated and need not be computed. Secondly, the final equations of motion are described in terms of a minimum number of generalized coordinates, this number being the degree of freedom of the system at hand. Finally, the problems associated with solving a system of differential and algebraic equations, which usually occurs when Lagrange multipliers are introduced, are avoided, since the constraints are incorporated naturally into the differential equations of motion. The above formulation is used to perform dynamic simulations of flexible-link mechanisms with a kinematic loop.

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