Kinematic analysis of Bricard’s mechanism

We show how the tools of computational algebra can be used to analyze the configuration space of multibody systems. One advantage of this approach is that the mobility can be computed without using the Jacobian of the system. As an example, we treat thoroughly the well-known Bricard’s mechanism, but the same methods can be applied to a wide class of rigid multibody systems. It turns out that the configuration space of Bricard’s system is a smooth closed curve, which can be explicitly parametrized. Our computations also yield a new formulation of constraints which is better than the original one from the point of view of numerical simulations.

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