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Feasibility of motion laws for planar one degree of freedom linkage mechanisms at dead point configurations

机译：死点配置下平面一自由度联动机构运动规律的可行性

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摘要

This paper proposes an analytical solution of the Inverse Kinematics (IK) problem at dead point configurations for any planar one degree of freedom linkage mechanism, with regard to the continuity C" of the motion law. The systems analyzed are those whose elements are linked with lower pairs and do not present redundancies. The study aims to provide the user with some rules to facilitate the design of feasible motion profiles to be reproduced by conventional electrical actuators at these configurations. During the last decades, several methods and techniques have been developed to study this specific configuration. However, these techniques are mainly focused on solving numerically the IK indeterminacy, rather than analyzing the motion laws that the mechanisms are able to perform at these particular configurations. The analysis presented in this paper has been carried out differentiating and applying l'Hopital's rule to the system of constraint equations φ(q) of the mechanism. The study also considers the feasibility of the time-domain profiles to be reproduced with conventional electrical actuators (i.e. AC/DC motors, linear actuators, etc.). To show the usefulness and effectiveness of the method, the development includes the analytical application and numerical simulations for two common one degree of freedom systems: a slider-crank and a four linkage mechanisms. Finally, experimental results are presented on a four linkage mechanism test bed.
机译：针对运动定律的连续性C“，提出了一种平面任意自由度联动机构在死点配置下的逆运动学（IK）问题的解析解。本研究旨在为用户提供一些规则，以帮助设计可行的运动曲线，以便在这些配置下由常规电动执行器再现这些运动曲线。研究这种特定的配置，但是这些技术主要侧重于数值求解IK不确定性，而不是分析机制在这些特定配置下能够执行的运动定律，本文所进行的分析已经进行了区分和应用。机构约束方程φ（q）系统的l'Hopital规则。 y还考虑了使用传统的电动执行器重现时域轮廓的可行性（即AC / DC马达，线性执行器等）。为了显示该方法的有效性和有效性，开发内容包括两个常见的一个自由度系统的分析应用程序和数值模拟：滑块曲柄和四个连杆机构。最后，在四连杆机构测试床上展示了实验结果。

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