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From sliding-rolling loci to instantaneous kinematics: An adjoint approach

机译:从滚动轨迹到瞬时运动学:一种伴随方法

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The adjoint approach has proven effective in studying the properties and distribution of coupler curves of crank-rocker linkages and the geometry of a rigid object in spatial motion. This paper extends the adjoint approach to a general surface and investigates kinematics of relative motion of two rigid objects that maintain sliding-rolling contact. We established the adjoint curve to a surface and obtained the fixed-point condition, which yielded the geometric kinematics of an arbitrary point on the moving surface. After time was taken into consideration, the velocity of the arbitrary point was obtained by two different ways. The arbitrariness of the point results in a set of overconstrained equations that give the translational and angular velocities of the moving surface. This novel kinematic formulation is expressed in terms of vectors and the geometry of the contact loci. This classical approach reveals the intrinsic kinematic properties of the moving object. We then revisited the classical example of a unit disc rolling-sliding on a plane. A second example of two general surfaces maintaining rolling-sliding contact was further added to illustrate the proposed approach. (C) 2014 Elsevier Ltd. All rights reserved.
机译:伴随方法已被证明可有效地研究曲柄摇杆连杆的耦合曲线的特性和分布以及空间运动中刚性物体的几何形状。本文将伴随方法扩展到一般曲面,并研究了两个保持滑动滚动接触的刚性物体的相对运动运动学。我们建立了曲面上的伴随曲线,并获得了定点条件,从而得出了运动面上任意点的几何运动学。在考虑时间之后,通过两种不同方式获得任意点的速度。该点的任意性导致了一组过度约束的方程,这些方程给出了移动表面的平移和角速度。这种新颖的运动学公式用矢量和接触位点的几何形状表示。这种经典方法揭示了运动物体的固有运动学特性。然后,我们回顾了在平面上滚动滑动的单位圆盘的经典示例。进一步添加了两个一般表面保持滚动滑动接触的第二个示例,以说明所提出的方法。 (C)2014 Elsevier Ltd.保留所有权利。

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