Abstract
It is well known in planar kinematics of rigid bodies that the acceleration of the material point coinciding with the instantaneous center of rotation (or pole) is perpendicular to the so-called pole changing velocity. In the present paper, the concept of pole changing velocity is generalized to spatial motions. Using this result, the acceleration of the material points along the instantaneous screw axis can be expressed in a straightforward way, without the tools of advanced differential geometry.
Highlights
Rigid body kinematics is a subject that belongs partly to geometry, partly to dynamics
The present paper focuses on the pole changing velocity that characterizes the change of the geometric position of the instantaneous center of rotation in the case of planar motions and nonzero angular velocity
The novelty of the proposed approach lies in the fact that the results are derived using Euler’s rigid body formulas (1), (2) and that the concept of pole changing velocity is generalized to spatial motions
Summary
Rigid body kinematics is a subject that belongs partly to geometry, partly to dynamics. The present paper focuses on the pole changing velocity that characterizes the change of the geometric position of the instantaneous center of rotation (or pole) in the case of planar motions and nonzero angular velocity. The goal of this contribution is to show that the concept of pole changing velocity can be generalized to spatial motions by using Euler’s rigid body formulas and exploiting that all motions can be interpreted as rolling or sliding of two ruled surfaces on each other. Csernák MTA-BME Research Group on Dynamics of Machines and Vehicles, Budapest, Hungary
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