Abstract
In both planar and spatial parallel mechanisms, selection of the structural parameters for a desired workspace generally employs the use of numerical methods. However, using the closed-form solution, if it exists, facilitates workspace-based design and optimization of the mechanism, and may significantly reduce the required time and calculation for finding the workspace of the mechanism. This paper presents a general and comprehensive closed-form solution for the reachable workspace of a 2-RPR planar parallel mechanism. The workspace of the mechanism is analyzed step-by-step in detail and its boundary is derived analytically. Since the solution is closed-form, it has high accuracy and reliability. Furthermore, the provided solution can be employed to solve the workspace of similar mechanisms in a closed-form manner including other n-RPR planar parallel mechanisms.
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