Kinematic analysis of a PPPR spatial serial mechanism with geometric errors

Abstract

The present study focuses on the kinematic analysis of a PPPR spatial serial mechanism with a large number of geometric errors. The study is implemented in three steps: (1) development of a map between the end-effector position error and geometric source errors within the serial mechanism kinematic chains using homogeneous transformation matrix; (2) selection of geometric errors which have significant effects on end-effector positioning accuracy by sensitivity analysis; (3) kinematic analysis of the serial mechanism within which the geometric errors are modelled as interval variables. The computational algorithms are presented for positioning accuracy analysis and workspace analysis in consideration of geometric errors. The analysis results show that the key factors which have significant effects on end-effector position error can be identified efficiently, and the uncertain workspace can also be calculated efficiently.

Precision estimation of large space-borne parabolic antenna support structure

“…where, bold-italicT P j and bold-italicT R j are the homogeneous matrix of shaft that corresponds to the offset static and the deflection static, respectively. Rot and Trans are rotation and translation operators, 22 respectively. α j is the angle between plane O j ′ − x j ′ z j ′ and plane O j − x j z j .…”

“…In addition, the accuracy analysis solutions for serial, 21,22 single-loop, 23,24 general parallel, 25–28 planar multi-loop, 7,29,30 and simple spatial multi-loop mechanisms 20 need to solve the variables directly from constraint equation. However, the support structure is a complex spatial mechanism with multi-loop coupled each other, which belongs to the spatial multi-loop coupled mechanism.…”

Active Compensation Technology for the Target Measurement Error of Two-Axis Electro-Optical Measurement Equipment

“…Different from the above error sensitivity analysis methods, which were carried out in the global coordinate system, the quantitative interval sensitivity analysis method was presented, and the key geometric errors were identified at different intervals [ 9 ]. Furthermore, for the robot, Feng used a homogeneous transformation matrix to develop the mapping relationship between the end-effector position error and geometric source errors within the serial mechanism kinematic chains, and studied the kinematics of the spatial serial mechanism with a large number of geometric errors [ 10 ]. Li used a full matrix complete differential method to construct the error model of a cable-driven parallel robot, the results confirmed that the cable length errors and pulleys’ geometric errors should be given higher priority in design [ 11 ].…”