This paper investigates the location of a rigid body such that specified points of the body lie on given planes in space. Variants of this problem arise in kinematics, metrology, and computer vision, including some, such as the motion of a spherical four-bar, that are not at first glance point-plane contact problems. The case , the minimum number to fully constrain the body, is of special interest: We give an eigenvalue method for finding all solutions, which may number up to eight. For there are, in general, no solutions, but if the constraints are compatible and not degenerate, we show how to find the unique solution by a linear least-squares method. For , the body is underconstrained, having in general degrees of freedom; we determine the degree of the general motion for each case. We also examine the workspace of a particular three-degree-of-freedom parallel-link tripod mechanism.
Issue Section:
Research Papers
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.Copyright © 2006
by American Society of Mechanical Engineers
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