In previous work (2001), we identified a class of robot grippers that can orient and grasp parts using an arrangement of trapezoidal jaw modules. In this paper, we define a parametric tolerance class for the jaws, such that the part alignment is guaranteed for all jaw geometry in the class. This tolerance class is derived based on the analysis of toppling, motion trajectory, and form-closure. We describe the O(n log n) algorithm to compute the parametric tolerance class based on maximal and minimal jaw specifications. We implemented the algorithm and report the results of physical experiments.
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