For motion planning with limited translations the c

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Unformatted text preview: their nominal positions. (b) The configuration space obstacle P7 \ P4 (thick curve), its tolerance envelope (thin curve), and the cone of blocked translation directions. 2. A cycle of Nc parts has exactly Nc-2 edges of weight 3, one edge of weight 2, and one edge of weight 1. The last two edges divide the cycle into two non-intersecting sets of parts X and Y connected by the edges. The relative position between parts connected by edges of weight 1 or 2 cannot be determined because it is underconstrained, but the relative positions between the rigid bodies corresponding to X and Y is well constrained. Figure 3 shows the sets X, Y for the assembly in Figure 1. Table 1 shows the algorithm to compute sensitivity matrices of part Pj relative to Pi. The algorithm computes the relative position transformations between pairs of parts on the path from Pi to Pj, and from them computes the sensitivity matrices. Its complexity is O(njqrij), where nj is the complexity of Pj, q is the maximal number of parameters affecting a single ve...
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