In determining the screw systems associated with incompletely specified displacements, the displacement of a line was known to be an exceptional case. Recent research has concluded that all possible screws for the finite displacement of a line do not form a screw system. This paper utilizes Dimentberg’s definition of pitch to demonstrate that all possible screws for displacing a line from one position to another can indeed form a screw system of the third order. Two different approaches are taken: one uses the concept of a screw triangle, and the other is based on analytical geometry. A set of three linearly independent screws of the screw system is shown to be perpendicularly intersecting the external bisector of the initial and final positions of the line.
The Finite Screw System Associated With the Displacement of a Line
Contributed by the Mechanisms and Robotics Committee for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 2001. Associate Editor: M. Raghavan.
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Huang, C., and Wang, J. (March 21, 2003). "The Finite Screw System Associated With the Displacement of a Line ." ASME. J. Mech. Des. March 2003; 125(1): 105–109. https://doi.org/10.1115/1.1539510
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