Inverse and forward kinematics and workspace analysis of a novel 5-DOF (3T2R) parallel–serial (hybrid) manipulator

Abstract

The proposed study provides a solution of the inverse and forward kinematic problems and workspace analysis for a five-degree-of-freedom parallel–serial manipulator, in which the parallel kinematic chain is made in the form of a tripod and the serial kinematic chain is made in the form of two carriages displaced in perpendicular directions. The proposed manipulator allows to realize five independent movements—three translations and two rotations motion pattern (3T2R). Analytical relationships between the coordinates of the end-effector and five controlled movements provided by manipulator’s drives (generalized coordinates) were determined. The approach of reachable workspace calculation was defined with respect to available design constraints of the manipulator based on the obtained algorithms of the inverse and forward kinematics. Case studies are considered based on the obtained algorithms of inverse and forward kinematics. For the inverse kinematic problem, the solution is obtained in accordance with the given laws of position and orientation change of the end-effector, corresponding to the motion along a spiral-helical trajectory. For the forward kinematic problem, various assemblies of the manipulator are obtained at the same given values of the generalized coordinates. An example of reachable workspace designing finalizes the proposed study. Dimensions and extreme values of the end-effector orientation angles are calculated.

Design and Motion Principle Analysis of new parallel mechanisms with fewer active inputs than the degrees of freedom

“…As shown in Figure 1a, in the first step, the lockable P joint on the first branch L 1 is released, while the other five branches L 2 to L 6 are locked. Since the length of the six passive branches are given, that is, l 1 = l 1t and l i = l i 0 $$(i=2,3,{\rm{\cdots }},6)$$, the posture of the moving platform can be obtained by solving the forward position model of the PM through Newton's iteration method (Antonov et al, 2021; Nag et al, 2021). When the posture of the moving platform is obtained, the adjustment amount of the driving branch l 7 can be obtained based on Equation (1).…”

“…First, by taking the target length l i of branch L 1 and initial lengths of branches L 2 ~ L 6 as inputs, the position and orientation of the moving platform, after the first passive branch is driven to the target length, can be obtained by solving the forward kinematic solution of the original 6SPS PM. In this work, the numerical iteration method is used to solve this problem (Antonov et al, 2021; Hou et al, 2020; Lu et al, 2020; Nag et al, 2021; Wu et al, 2021; Ye et al, 2020; Zhang et al, 2021), the detailed calculation procedures will not be elaborated here. Next, the length l 71 of L 7 is calculated based on the inverse kinematic solution of the entire PM.…”

Kinematics of the Hybrid 6-Axis (H6A) manipulator

“…The corresponding singularity is studied as Case 5 in Section 6.2. 18 It is worth mentioning that if cos β sin θ α 1 = 0 (the term (a 6 − l w cos κ) cannot vanish for the values of architecture parameters chosen in this article (see Table III)) an alternative procedure requiring the calculation of sin θ γ 7 from ( 27) is to be pursued. The process, being very similar to the one used above, is explained very briefly for the sake of completeness.…”

“…The forward and inverse kinematics of a 3T2R parallel-serial (hybrid) manipulator are presented in ref. [18]. Yet another 5-axis hybrid robot, the TriMule, was analysed for its inverse kinematics and singularities in ref.…”

Kinematics and dynamics analysis of a six-degree of freedom parallel manipulator

“…In practice, an aircraft model will move along the given trajectory, which usually contains pitch, roll, yaw, heave, surge, and sway motion about the reference coordinate system, so a kind of 6-DOF mechanisms with high precision and stabilization are required to achieve the demands of corresponding tests. 1,2 Parallel manipulators are closed-loop mechanical structures composed of a moving platform coupled to a fixed base by serial limbs, which usually can provide multi-degree of freedom with great comprehensive performance, 3,4 and they will be a good choice for wind tunnel tests.…”