This paper aims at exploiting the unique characteristics of instantaneous invariants and pole locations in synthesizing motion generation four bar (4R) planar mechanisms with higher-order coupler point kinematics (i.e. specifying coupler point velocity and/or acceleration in addition to its position and coupler orientation). The proposed methodology targets to ease the complexity of such design problems by reducing the number of non-linear governing equations that are solved to generate the desired dyads of the final 4R mechanism design. The new approach integrates graphical and analytical techniques to synthesize 4R mechanisms with prescribed coupler point position, velocity, and acceleration. Two case studies are presented; the first presents the synthesis of a motion generation 4R with 3 prescribed coupler point positions and 2 prescribed coupler point velocities; the second presents the synthesis of a motion generation 4R with 2 prescribed coupler point positions, 2 prescribed coupler point velocities, and 1 prescribed coupler point acceleration. When compared to classical kinematic-based approaches, the proposed method prominently reduces the size and complexity of the set of governing non-linear equations.

中文翻译：

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利用曲率理论的瞬时不变量进行高阶耦合点运动学 4R 机构的运动生成综合

本文旨在利用瞬时不变量和极点位置的独特特征来合成具有高阶耦合点运动学的运动生成四杆（4R）平面机构（即除了位置和耦合器方向之外还指定耦合点速度和/或加速度） ）。所提出的方法旨在通过减少非线性控制方程的数量来简化此类设计问题的复杂性，这些非线性控制方程的求解可生成最终 4R 机构设计所需的二元组。新方法集成了图形和分析技术，以合成具有指定耦合点位置、速度和加速度的 4R 机构。提出了两个案例研究；第一个展示了具有 3 个指定耦合器点位置和 2 个指定耦合器点速度的运动生成 4R 的合成；第二个展示了具有 2 个指定耦合器点位置、2 个指定耦合器点速度和 1 个指定耦合器点加速度的运动生成 4R 的合成。与经典的基于运动学的方法相比，所提出的方法显着降低了控制非线性方程组的大小和复杂性。