Abstract
Kinematic accuracy is a crucial indicator for evaluating the performance of mechanisms. Low-mobility parallel mechanisms are examples of parallel robots that have been successfully employed in many industrial fields. Previous studies analyzing the kinematic accuracy analysis of parallel mechanisms typically ignore the randomness of each component of input error, leading to imprecise conclusions. In this paper, we use homogeneous transforms to develop the inverse kinematics models of an improved Delta parallel mechanism. Based on the inverse kinematics and the first-order Taylor approximation, a model is presented considering errors from the kinematic parameters describing the mechanism’s geometry, clearance errors associated with revolute joints and driving errors associated with actuators. The response surface method is employed to build an explicit limit state function for describing position errors of the end-effector in the combined direction. As a result, a mathematical model of kinematic reliability of the improved Delta mechanism is derived considering the randomness of every input error component. And then, reliability sensitivity of the improved Delta parallel mechanism is analyzed, and the influences of the randomness of each input error component on the kinematic reliability of the mechanism are quantitatively calculated. The kinematic reliability and proposed sensitivity analysis provide a theoretical reference for the synthesis and optimum design of parallel mechanisms for kinematic accuracy.
Highlights
A parallel robot has the advantages of high structural stiffness, high precision of both position and pose, low manufacturing and control cost, etc
Dragos et al researched the influence of dimensional deviations, kinematic joints clearances and input errors introduced by the actuator on the positioning accuracy of the 3-DOF Delta parallel robots [23,24,25]
Based on kinematic reliability and its sensitivity analysis, this paper aims to find out the crucial indicator for evaluating the performance of mechanisms to improve the kinematic reliability of the robot
Summary
A parallel robot has the advantages of high structural stiffness, high precision of both position and pose, low manufacturing and control cost, etc. Dragos et al researched the influence of dimensional deviations, kinematic joints clearances and input errors introduced by the actuator on the positioning accuracy of the 3-DOF Delta parallel robots [23,24,25]. Chen et al researched the actuator input selection and optimization of the parallel mechanism, and evaluated the motion stability of each actuator [27]; Amir et al presented analytical approach for the dimensional synthesis of the 3-DOF Delta parallel robot for a prescribed workspace [28]. The kinematic accuracy analysis of mechanisms is mainly focused on method involving the modeling of static position and pose errors. The main contributions of this paper are as follows: (1) In the previous study, kinematic accuracy analysis of the improved Delta parallel mechanism usually ignores the randomness of each input error component. Compared to the traditional reliability sensitivity analysis of the parallel mechanisms, the new method for reliability sensitivity analysis proposed in this paper is available even if the ultimate state function i.e., the real analytical response expression of the mechanical system is unknown
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