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

• Published in: Mechanical systems and signal processing Vol. 98; pp. 834 - 851
• Main Authors: Lores García, E., Veciana Fontanet, J.M., Jordi Nebot, L.
• Format: Journal Article Publication
• Language: English
• Published: Berlin Elsevier Ltd 01-01-2018; Elsevier BV
• Subjects: A C motors; Actuators; Cinemàtica; Computer simulation; Configuration management; Configurations; D C motors; Dead point; Degrees of freedom; Electric motors; Enginyeria mecànica; Feasibility studies; Inverse kinematics; Kinematics; Linkage mechanism; Linkage mechanisms; Mathematical analysis; Mechanical movements; Mecànica; Motion effects; Motion law; Motors; Moviments mecànics; Simulation; Singular configuration; Studies; Àrees temàtiques de la UPC; Dead point; Singular configuration; Motion law; Inverse kinematics; Linkage mechanism
• DOI: 10.1016/j.ymssp.2017.05.015
• EISSN: 1096-1216
• ISSN: 0888-3270

•The continuity condition of a motion law is analyzed at dead point configurations.•The feasibility of the laws is imposed to be reproduced by electrical actuators.•The Inverse Kinematics problem is arised trying to obtain an analytical solution.•L’Hôpital’s rule is applied to the system of constraint equations of the mechanism.•The proposed solution is valid for any planar one degree of freedom mechanism.
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 Cn 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’Hôpital’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.