Exploiting the Kinematic Redundancy of a 6+3 Dofs Parallel Mechanism

2018 ◽  
Author(s):  
Louis-Thomas Schreiber ◽  
Clément Gosselin
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Stewart Platform ◽  
Kinematic Redundancy ◽  
Compressive Loads ◽  
Planning Methods ◽  
Moving Platform

This paper presents trajectory planning methods for a kinematically redundant parallel mechanism. The architecture of the mechanism is similar to the well-known Gough-Stewart platform and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The kinematic redundancy is exploited to avoid singularities and extend the rotational workspace. The architecture is described and the associated kinematic relationships are presented. Solutions for the inverse kinematics are given, as well as strategies to take into account the limitations of the mechanism such as mechanical interferences and velocity limits of the actuators while controlling the redundant degrees of freedom.

Exploiting the Kinematic Redundancy of a (6 + 3) Degrees-of-Freedom Parallel Mechanism

2019 ◽  
Vol 11 (2) ◽  
Author(s):  
Louis-Thomas Schreiber ◽  
Clément Gosselin
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Kinematic Redundancy ◽  
Spatial Parallel Mechanism ◽  
Compressive Loads ◽  
Moving Platform

This paper presents methods to exploit the redundancy of a kinematically redundant spatial parallel mechanism with three redundant DOFs. The architecture of the mechanism is similar to the well-known Gough–Stewart (GS) platform and it retains its advantages, i.e., the members connecting the base to the moving platform are only subjected to tensile/compressive loads. The kinematic redundancy is exploited to avoid singularities and extend the rotational workspace. The architecture is described and the associated kinematic relationships are presented. Solutions for the inverse kinematics are given, as well as strategies to take into account the limitations of the mechanism such as mechanical interferences and velocity limits of the actuators while controlling the redundant degrees-of-freedom.

A Novel Three-DOF 3-RRRRR Parallel Platform Mechanism and Its Position Analysis

2005 ◽  
Author(s):  
Shihua Li ◽  
Zhen Huang ◽  
Jianguang Wu
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Initial Configuration ◽  
Parallel Platform ◽  
Moving Platform ◽  
General Configuration ◽  
Novel Model ◽  
Three Degrees Of Freedom

In order to enrich deficient-DOF parallel mechanism models, a novel model of a 3-DOF platform manipulator is presented and establish its inverse kinematics equation. Here, studies instantaneous motions of 3-RRRRR parallel manipulator at initial configuration and general configuration. Find: it has three degrees of freedom at initial configuration and after translated along the X, Y, Z axis. Secondly, the relation is given between every active input (θ1) and moving platform position by using D-H means, the solution is developed for inverse kinematics, numerical example for the position kinematic is presented, the figure of workspace along the Z-axis is drawn finally. The mechanism can be applied to jiggle mechanism.

scholarly journals Reconfiguration Analysis of a 3-DOF Parallel Mechanism

Robotics ◽  
2019 ◽  
Vol 8 (3) ◽  
pp. 66
Author(s):  
Maurizio Ruggiu ◽  
Xianwen Kong
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Operation Mode ◽  
Parallel Mechanisms ◽  
Universal Joint ◽  
Kinematic Chains ◽  
Constraint Equations ◽  
The Third ◽  
Equilateral Triangles ◽  
Moving Platform

This paper deals with the reconfiguration analysis of a 3-DOF (degrees-of-freedom) parallel manipulator (PM) which belongs to the cylindrical parallel mechanisms family. The PM is composed of a base and a moving platform shaped as equilateral triangles connected by three serial kinematic chains (legs). Two legs are composed of two universal (U) joints connected by a prismatic (P) joint. The third leg is composed of a revolute (R) joint connected to the base, a prismatic joint and universal joint in sequence. A set of constraint equations of the 1-RPU−2-UPU PM is derived and solved in terms of the Euler parameter quaternion (a.k.a. Euler-Rodrigues quaternion) representing the orientation of the moving platform and of the Cartesian coordinates of the reference point on the moving platform. It is found that the PM may undergo either the 3-DOF PPR or the 3-DOF planar operation mode only when the base and the moving platform are identical. The transition configuration between the operation modes is also identified.

scholarly journals Design and Analysis of a Flexible, Elastic, and Rope-Driven Parallel Mechanism for Wrist Rehabilitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Zaixiang Pang ◽  
Tongyu Wang ◽  
Junzhi Yu ◽  
Shuai Liu ◽  
Xiyu Zhang ◽  
...  
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Inverse Kinematic ◽  
Parallel Structure ◽  
Flexible Joints ◽  
Rehabilitation Robots ◽  
Hybrid Mechanism ◽  
Compression Spring ◽  
Moving Platform

This paper proposes a bionic flexible wrist parallel mechanism to simulate human wrist joints, which is characterized by a rope-driven, compression spring-supported hybrid mechanism. Specifically, to realize the movement of the wrist mechanism, a parallel structure is adopted to support the mobile platform and is controlled by a cable, which plays the role of wrist muscles. Because the compression spring is elastic, it is difficult to directly solve inverse kinematics. To address this problem, the external force acting on the moving platform is firstly equivalent to the vector force and torque at the center of the moving platform. Then, based on inverse kinematic and static analyses, the inverse motion of the robot model can be solved according to the force and torque balance conditions and the lateral spring bending equation of the compression spring. In order to verify the proposed method, kinematics, statics, and parallel mechanism workspace are further analyzed by the software MATLAB. The obtained results demonstrate the effectiveness and feasibility of the designed parallel mechanism. This work offers new insights into the parallel mechanism with flexible joints in replicating the movements of the human wrist, thus promoting the development of rehabilitation robots and rope-driven technology to some extent.

Orientation Workspace Analysis of a Novel 3SPS+1PS Symmetrical Parallel Manipulator Based on Unit Quaternion

2011 ◽  
Vol 201-203 ◽  
pp. 1849-1853
Author(s):  
Jing Li Yu ◽  
Gang Cheng ◽  
Shuai Zhang ◽  
De Kun Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Unit Quaternion ◽  
Structure Characteristics ◽  
Workspace Analysis ◽  
Moving Platform ◽  
Position And Orientation ◽  
4 Degrees Of Freedom ◽  
Orientation Workspace

For a novel 3SPS+1PS parallel manipulator with 4 degrees of freedom including three rotations and one translation, the formulae for solving the inverse kinematics equations are derived based on quaternion method. Unit quaternion is used to represent the position and orientation of moving platform, and the singularities caused by Euler angles are avoided. Combining the topological structure characteristics of the parallel manipulator, it only has three rotations when its moving platform is at a given translation position. Based on the inverse position/pose equations and the all the constraints of the parallel manipulator, the discrete algorithm for the orientation workspaces of 3SPS+1PS parallel manipulator where the moving platform is at some different given translation positions are designed. The research builds the theoretical basis for optimizing the orientation workspace with given position.

scholarly journals Simulation of a parallel mechanical elbow with 3 DOF

2009 ◽  
Vol 7 (02) ◽  
Author(s):  
J. R. Mendoza-Vázquez ◽  
E. Tlelo-Cuautle ◽  
J.L. Vázquez-Gonzalez ◽  
A. Z. Escudero-Uribe
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Mechanical Support ◽  
Simulation And Modeling ◽  
Matlab Simulation ◽  
Geometric Methods ◽  
Kinematics Simulation ◽  
Linear Actuators ◽  
Simulation Results

The kinematics simulation and modeling of a mechanical elbow of 3 degrees of freedom, is introduced by highlighting the main features of the mechanism related to the design criteria. The mechanical elbow is used as a transhumeral prosthetic part, and it has been built as a parallel topology consisting of electric linear actuators and universal joints. The parallel mechanism has 4 legs. 3 are electric linear actuators, and the fourth leg provides mechanical support for the whole structure and holds a DC Motor that performs the action of gripping objects. Furthermore, this paper shows the inverse kinematics for the elbow by geometric methods, and the MatLab‐simulation results show the workspace of the movement and the ability of the mechanical elbow to replicate the movements of a biological one.

Influence Coefficients and Singularity Analysis of a Novel 3-UPU Parallel Mechanism

2017 ◽  
Author(s):  
Ziming Chen ◽  
Dongliang Cheng ◽  
Yang Zhang ◽  
Zhiwei Yang ◽  
Jin Zhou
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Model Simulation ◽  
Hessian Matrix ◽  
Symmetry Plane ◽  
Coefficient Matrix ◽  
Singularity Analysis ◽  
Influence Coefficient ◽  
Parasitic Motion ◽  
Moving Platform

A novel 3-UPU parallel mechanism with two rotational and one translational (2R1T) degrees of freedom (DOFs) is analyzed in this paper. The base and moving platform of this mechanism are always symmetric about a middle symmetry plane. The moving platform can rotate continuously about any axis on the middle symmetry plane, so there exists no parasitic motion during the rotation. Using the kinematic influence coefficient theory and the imaginary mechanism method, the first and second order influence coefficient matrix (namely Jacobian matrix and Hessian matrix) of this mechanism are derived. The relations between the velocity and acceleration of the moving platform and the actuated links are obtained. In order to verify the correctness of the theory, two numerical examples are enumerated and varified by the 3D model simulation. The singularities of this mechanism is discussed and the singular configurations of the mechanism, including one kind of limb singularity and two kinds of platform singularities, are obtained.

Analytical Trajectory Optimization of Seven Degrees of Freedom Redundant Robots

1987 ◽  
Vol 11 (4) ◽  
pp. 197-200 ◽  
Author(s):  
B. Benhabib ◽  
R.G. Fenton ◽  
A.A. Goldenberg
Keyword(s):  
Trajectory Planning ◽  
Trajectory Optimization ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Optimization Problem ◽  
Optimization Procedure ◽  
Redundant Robots ◽  
Point Motion ◽  
Point To Point ◽  
Lagrange’S Method

The basic characteristic of kinematically redundant robots is that non-unique joint solutions may exist for a specified end effector location. Thus, trajectory planning for a kinematically redundant robot requires an optimization procedure to determine the joint displacements when solving the inverse kinematics relations. In this paper an analytical solution is developed for the trajectory optimization problem of redundant robots based on the classical Lagrange’s method. A detailed formulation is provided for seven degrees of freedom robots, which minimizes the Euclidean norm of joint dislacements for point-to-point motion trajectory planning.

A Planar Spring-Loaded Cable-Loop-Driven Parallel Mechanism

2010 ◽  
Author(s):  
Hanwei Liu ◽  
Cle´ment Gosselin ◽  
Thierry Laliberte´
Keyword(s):  
Numerical Simulations ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Static Equilibrium ◽  
Equilibrium Equations ◽  
Two Degrees Of Freedom

A novel architecture of planar spring-loaded cable-loop-driven parallel mechanism is introduced in this paper. By attaching springs to the cable loops, two degrees of freedom can be controlled using only two actuators. In this mechanism, spools are eliminated. Therefore, it is expected that the accuracy of this mechanism is improved compared with conventional cable-driven mechanisms making use of spools. The mechanism can be actuated using either linear sliders or rotary actuators driving the motion of a cable or belt. This paper presents the inverse kinematics and the static equilibrium equations for the new architecture. It is verified that the cables and the springs can be kept in tension within the workspace. Results of numerical simulations are also given.

Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator

2021 ◽  
Vol 11 (20) ◽  
pp. 9438
Author(s):  
Jianwei Zhao ◽  
Tao Han ◽  
Xiaofei Ma ◽  
Wen Ma ◽  
Chengxiang Liu ◽  
...  
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Random Number ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Joint Space ◽  
Work Requirements ◽  
Multiple Degrees Of Freedom ◽  
Quintic Polynomial

To address the problems of mismatch, poor flexibility and low accuracy of ordinary manipulators in the complex special deflagration work process, this paper proposes a new five-degree-of-freedom (5-DOF) folding deflagration manipulator. Firstly, the overall structure of the explosion-expulsion manipulator is introduced. The redundant degrees of freedom are formed by the parallel joint axes of the shoulder joint, elbow joint and wrist pitching joint, which increase the flexibility of the mechanism. Aiming at a complex system with multiple degrees of freedom and strong coupling of the manipulator, the virtual joint is introduced, the corresponding forward kinematics model is established by D–H method, and the inverse kinematics solution of the manipulator is derived by analytical method. In the MATLAB platform, the workspace of the manipulator is analyzed by Monte Carlo pseudo-random number method. The quintic polynomial interpolation method is used to simulate the deflagration task in joint space. Finally, the actual prototype experiment is carried out using the data obtained by simulation. The trajectory planning using the quintic polynomial interpolation method can ensure the smooth movement of the manipulator and high accuracy of operation. Furthermore, the trajectory is basically consistent with the simulation trajectory, which can realize the work requirements of putting the object into the explosion-proof tank. The new 5-DOF folding deflagration manipulator designed in this paper has stable motion and strong robustness, which can be used for deflagration during the COVID-19 epidemic.

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