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.
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January 2006
Research Papers
On a Rigid Body Subject to Point-Plane Constraints
Charles W. Wampler
e-mail: charles.w.wampler@gm.com
Charles W. Wampler
General Motors R&D Center
, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055
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Charles W. Wampler
General Motors R&D Center
, Mail Code 480-106-359, 30500 Mound Road, Warren, MI 48090-9055e-mail: charles.w.wampler@gm.com
J. Mech. Des. Jan 2006, 128(1): 151-158 (8 pages)
Published Online: July 19, 2005
Article history
Received:
April 29, 2005
Revised:
July 19, 2005
Citation
Wampler, C. W. (July 19, 2005). "On a Rigid Body Subject to Point-Plane Constraints." ASME. J. Mech. Des. January 2006; 128(1): 151–158. https://doi.org/10.1115/1.2120787
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