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Unformatted text preview: art) when B is positioned according to the specification and the variational 68 Y. Ostrovsky-Berman and L. Joskowicz parameters of both parts span their allowed values. For each vertex u of B, the goal is to compute the transformation matrix that describes the sensitivity of the vertex to variations in the parameters of parts A and B. The 2 × m sensitivity matrix Su has one column for each of the variational parameters. We first describe the relative position constraints and their associated equations. We then show how to solve the resulting system of equations and compute the sensitivity matrices of B. 2.2.1 Relative position constraints Planar part B has three degrees of freedom, two for translation and one for rotation. Thus, to uniquely determine its position relative to A, three independent constraints are required. For each instance of the parts, there is a rigid transformation T = (tx,ty,θ) that positions B relative to A and satisfies the constraints. Since the part variations are typically at least two orders of magnitude smaller than the nominal dimensions, we approximate the transformation angle with cos(θ)≈...
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This note was uploaded on 08/03/2010 for the course DD 1234 taught by Professor Zczxc during the Spring '10 term at Magnolia Bible.

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