Kinematics/statics and workspace analysis of a 3-leg 5-DoF parallel manipulator with a UPU-type composite active constrained leg

Abstract

SUMMARYA novel 3-leg 5-DoF parallel manipulator (PM) with a UPU-type composite active constrained leg is proposed and its kinematics and statics are analyzed systematically. First, the formulae are derived for solving the inverse/forward displacements, inverse/forward velocities, and active/constraint forces. Second, the formulae are derived for solving inverse/forward accelerations. Third, a simulation mechanism of this PM is created and its workspace is constructed and analyzed. Finally, the analytic results are verified by its simulation mechanism. The line from a i to o, e i = e.The line fromThe active leg and its length. l i , L i The side of m and B. P, S The prismatic joint and the spherical joint. R jThe revolute joints (j = 1, 2, 3, 4).The universal joint with R 1 and R 2. U BThe universal joint with R 3 and R 4. {m} Coordinate frame o-xyz fixed on m. {B} Coordinate frame O-XYZ fixed on B. v riThe input velocity of active leg. e, E The distances from a i to o and from A i to O. F, T The concentrated force and torque applied on m at o. F aiThe active forces applied on and along r i. T aThe active torque applied on R 1. T λThe active torque applied on R 4. F c , T c The constrained force and the constrained torque. T bThe bending moment exerted on r 2. Rotational matrix from {m} to {B}. J, HThe Jacobian matrix and Hessian matrix.

Kinematics and statics analysis of a novel 5-DoF parallel manipulator with two composite rotational/linear active legs

“…The results show that W of the 2UPSþ SPR PM is larger than that of the 4SPS þ SPR PM [16] and that of the 3-leg 5-DoF PM with a UPU-type composite active leg [18]. When set central point of m at X o ¼1.14, Y o ¼2.03, Z o ¼11.27 cm, three Euler angles (α, β, γ) can be varied in 1001 or more by giving r 2 ¼ 10, 11, 12, 13, 14, 14.5 cm, and varying r i , (i ¼1, 3), see Fig.…”

“…Meanwhile, it is has been a significant and challenging issue to establish their mathematic model of velocity, acceleration, statics and dynamics. Lu et al [17] proposed a 3-leg 5-DoF PM including two SPS-type active legs and a PRRPR composite leg with three actuators (the bold symbol represents active joint) and a 3-leg 5-DoF PM including two SPS-type active legs and one UPU-type composite active leg with three actuators [18], and studied their kinematics/statics and workspace. However, both the PRRPR-type and the UPU-type composite active legs are quite complicated in structure due to one composite leg including three actuators.…”

Analysis and Optimization of a Spatial Parallel Mechanism for a New 5-DOF Hybrid Serial-Parallel Manipulator

“…According to the reciprocal screw theory [27], we know that every limb of 2RPU/UPR PM exists a constraint force and a constraint couple. In each limb, the constraint force passes through the U joint and is parallel to the axis of R joint; and the constraint couple is perpendicular to all of the rotational axes.…”

Stiffness Characteristics Analysis of a Novel 3- DOF Parallel Kinematic Machine Tool

“…ai , ai f and $ ri , ri f (i=1,2,3,4) respectively. The second and fourth chain can provide the moving platform with constraint moment and amplitude $ i  , i f  (i=2, 4) , it can be also decomposed into two constraint moments along the driving link and perpendicular to the driving link direction [19].…”