Screw quantities provide geometric insight into three-dimensional mechanics modeled by rigid bodies and lumped parameters. Four distinct cases of time differentiation are examined by combining fixed and moving body derivatives (fundamental to rigid body mechanics) with material and local derivatives (fundamental to continuum mechanics). Three combinations always yield another screw quantity while the most common, the material derivative with respect to the fixed body, does not. Two fundamental formulations are examined with this last derivative, Euler’s Laws and the gravitational loading of an elastic system. By coincidence, the formulations appear screw-like when they are expressed at the center-of-mass but, in contrast to actual screw formulations, they do not retain invariant forms when expressed at arbitrary points.
- Design Engineering Division and Computers and Information in Engineering Division
Material and Local Time Derivatives of Screws With Applications to Dynamics and Stiffness
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Lipkin, H. "Material and Local Time Derivatives of Screws With Applications to Dynamics and Stiffness." Proceedings of the ASME 2004 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 2: 28th Biennial Mechanisms and Robotics Conference, Parts A and B. Salt Lake City, Utah, USA. September 28–October 2, 2004. pp. 1339-1348. ASME. https://doi.org/10.1115/DETC2004-57506
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