This paper studies the inverse static analysis of a planar parallel mechanism with compliant limbs. A known force and moment is applied to the moving platform, and it is required to determine the assembly configurations, or equilibrium points. Partial derivatives of the potential energy function yields the equilibrium conditions. The geometric and static constraints lead to a system of ten polynomials with ten unknowns. We use polynomial homotopy method to find that there are as many as 70 equilibrium configurations. Two examples with equilateral geometry are provided. We also examine the system behavior during a movement between selected equilibrium positions.

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