Solving the dynamic equations of a 3-PRS Parallel Manipulator for efficient model-based designs

Abstract

Abstract. Introduction of parallel manipulator systems for different applications areas has influenced many researchers to develop techniques for obtaining accurate and computational efficient inverse dynamic models. Some subject areas make use of these models, such as, optimal design, parameter identification, model based control and even actuation redundancy approaches. In this context, by revisiting some of the current computationally-efficient solutions for obtaining the inverse dynamic model of parallel manipulators, this paper compares three different methods for inverse dynamic modelling of a general, lower mobility, 3-PRS parallel manipulator. The first method obtains the inverse dynamic model by describing the manipulator as three open kinematic chains. Then, vector-loop closure constraints are introduced for obtaining the relationship between the dynamics of the open kinematic chains (such as a serial robot) and the closed chains (such as a parallel robot). The second method exploits certain characteristics of parallel manipulators such that the platform and the links are considered as independent subsystems. The proposed third method is similar to the second method but it uses a different Jacobian matrix formulation in order to reduce computational complexity. Analysis of these numerical formulations will provide fundamental software support for efficient model-based designs. In addition, computational cost reduction presented in this paper can also be an effective guideline for optimal design of this type of manipulator and for real-time embedded control.

Investigation of an Underwater Vectored Thruster Based on 3RPS Parallel Manipulator

“…e thrust-vectoring mechanism is designed based on 3-RPS manipulator, which has a top rotting platform, a fixed base, and three identical sets of driving limbs and joints. Each driving limb has an actuating prismatic joint (P) attached to the fixed base by a rotational joint (R) and connected to the platform by a spherical joint (S) [53][54][55]. Each limb is driven by a linear actuator.…”

A Numerical Approach for 3 PRS Parallel Manipulator

“…As an example of the forward kinematics solution for a 3-PRS manipulator, let the manipulator parameters be taken as L 1…”

“…Based on the previous research, most of the parallel manipulators forward and inverse kinematics solutions are solved in closed form [1] [2] and its solutions are compared by simulation results [3] [4][5] [6]. The kinematic design, architecture optimization and actuator layout angles of 3-PRS parallel manipulator are investigated based on the performance index and various simulation software packages are used to verify the results obtained [7][14] [15].…”

An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

“…The study of dynamic problems can be an effective guideline for optimal design of this type of manipulator and for real-time embedded control. 4 Unlike serial manipulators, an explicit dynamic formulation of the SPM is much more complicated due to the closed kinematic chain. The literature on dynamic modeling of PMs mainly falls into four categories: Euler–Lagrange formulation, 5,6 Newton–Euler laws, 8,9 Kane method, 10–12 the principle of virtual work, 13–16 and Gibbs–Appell equations.…”