scholarly journals Kinematic Analysis of the 3-RPS Cube Parallel Manipulator

2014 ◽  
Author(s):  
Latifah Nurahmi ◽  
Josef Schadlbauer ◽  
Manfred Husty ◽  
Philippe Wenger ◽  
Stéphane Caro
Keyword(s):  
Parallel Manipulator ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Joint Space ◽  
Geometric Interpretation ◽  
Design Parameters ◽  
Euclidean Group ◽  
Constraint Equations ◽  
Kinematic Mapping ◽  
Three Degree Of Freedom

The 3-RPS Cube parallel manipulator, a three-degree-of-freedom parallel manipulator initially proposed by Huang et al. in 1995, is analysed in this paper with an algebraic approach, namely Study kinematic mapping of the Euclidean group SE(3) and is described by a set of eight constraint equations. A primary decomposition is computed over the set of eight constraint equations and reveals that the manipulator has only one operation mode. Inside this operation mode, it turns out that the direct kinematics of the manipulator with arbitrary values of design parameters and joint variables, has sixteen solutions in the complex space. A geometric interpretation of the real solutions is given. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular poses are mapped onto the joint space and are geometrically interpreted. By parametrizing the set of constraint equations under the singularity conditions, it is shown that the manipulator is in actuation singularity. The uncontrolled motion gained by the platform is also provided.

scholarly journals Kinematic Analysis of the 3-RPS Cube Parallel Manipulator

2015 ◽  
Vol 7 (1) ◽  
Author(s):  
Latifah Nurahmi ◽  
Josef Schadlbauer ◽  
Stéphane Caro ◽  
Manfred Husty ◽  
Philippe Wenger
Keyword(s):  
Intelligent Systems ◽  
Parallel Manipulator ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Joint Space ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Rotational Axis ◽  
Constraint Equations ◽  
Moving Platform

The 3-RPS cube parallel manipulator, a three-degree-of-freedom parallel manipulator initially proposed by Huang and Fang (1995, “Motion Characteristics and Rotational Axis Analysis of Three DOF Parallel Robot Mechanisms,” IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, Vancouver, BC, Canada, Oct. 22–25, pp. 67–71) is analyzed in this paper with an algebraic approach, namely, Study kinematic mapping of the Euclidean group SE(3) and is described by a set of eight constraint equations. A primary decomposition is computed over the set of eight constraint equations and reveals that the manipulator has only one operation mode. Inside this operation mode, it turns out that the direct kinematics of the manipulator with arbitrary values of design parameters and joint variables, has 16 solutions in the complex space. A geometric interpretation of the real solutions is given. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular poses are mapped onto the joint space and are geometrically interpreted. By parametrizing the set of constraint equations under the singularity conditions, it is shown that the manipulator is in actuation singularity. The uncontrolled motion gained by the moving platform is also provided. The motion of the moving platform is essentially determined by the fact that three vertices in the moving platform move in three mutually orthogonal planes. The workspace of each point of the moving platform (with exception of the three vertices) is bounded by a Steiner surface. This type of motion has been studied by Darboux in 1897. Moreover, the 3DOF motion of the 3-RPS cube parallel manipulator contains a special one-degree-of-freedom motion, called the vertical Darboux motion (VDM). In this motion, the moving platform can rotate and translate about and along the same axis simultaneously. The surface generated by a line in the moving platform turns out to be a right-conoid surface.

scholarly journals Operation Modes and Singularities of 3-PRS Parallel Manipulators With Different Arrangements of P-Joints

2015 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro ◽  
Philippe Wenger
Keyword(s):  
Algebraic Approach ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Euclidean Group ◽  
Constraint Equations ◽  
Operation Modes ◽  
Prismatic Joints ◽  
Kinematic Mapping ◽  
The Subject ◽  
Orientation Workspace

The subject of this paper is about the study of the operation modes and the singularity conditions of the 3-PRS parallel manipulator with different arrangements of prismatic joints. The three prismatic joints of the PRS legs are attached to the base with an angle α between the horizontal plane of the base and their directions. By using an algebraic approach, namely the Study kinematic mapping of the Euclidean group SE(3), the mechanisms are described by a set of eight constraint equations. A primary decomposition is computed over a set of eight constraint equations and reveals that the 3-PRS manipulators with different arrangements of prismatic joints have identical operation modes, namely x0 = 0 and x3 = 0. Both operation modes are analysed. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular configurations are mapped onto the joint space and are geometrically interpreted. The singularity loci of the 3-PRS parallel manipulators are also traced in its orientation workspace for different values of angle α.

scholarly journals Operation Modes Comparison of a Reconfigurable 3-PRS Parallel Manipulator Based on Kinematic Performance

2016 ◽  
Author(s):  
Siddharth Maraje ◽  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Transmission Efficiency ◽  
Force Transmission ◽  
Operation Modes ◽  
Transmission Index ◽  
Prismatic Joints ◽  
Kinematic Mapping

The 3-PRS parallel manipulator with different arrangements of prismatic joints is called a reconfigurable 3-PRS parallel manipulator in this paper. The three prismatic joints in PRS limbs are attached to the base with an angle α between the horizontal plane of the base and their directions. Based on [1], the manipulator has identical operation modes, namely x0 = 0 and x3 = 0 for any value of α. Accordingly, this paper presents in more details the performance evaluation of these operation modes by using the output transmission index (OTI) and the constraint transmission index (CTI). The OTI and CTI determine the force transmission efficiency and the constraining ability of the manipulators, respectively. Initially, the determination of the number and types of operation modes of the 3-PRS parallel manipulator is recalled. The computation is carried out by using an algebraic approach, namely the Study kinematic mapping. In each operation mode, the actuation wrenches and the constraint wrenches are obtained based on the Screw theory. Then, the OTI and CTI are traced in the orientation workspace of the manipulator for different values of angle α. Furthermore, the singularity conditions are analysed corresponding to the values of OTI and CTI.

scholarly journals Kinematic analysis of a single-loop reconfigurable 7R mechanism with multiple operation modes

Robotica ◽  
2014 ◽  
Vol 32 (7) ◽  
pp. 1171-1188 ◽  
Author(s):  
Xiuyun He ◽  
Xianwen Kong ◽  
Damien Chablat ◽  
Stéphane Caro ◽  
Guangbo Hao
Keyword(s):  
Kinematic Analysis ◽  
Computer Aided Design ◽  
Operation Mode ◽  
Algebraic Approach ◽  
Single Loop ◽  
Operation Modes ◽  
Translational Mode ◽  
Kinematic Mapping ◽  
Multiple Operation ◽  
Aided Design

SUMMARYThis paper presents a novel one-degree-of-freedom (1-DOF) single-loop reconfigurable 7R mechanism with multiple operation modes (SLR7RMMOM), composed of seven revolute (R) joints, via adding a revolute joint to the overconstrained Sarrus linkage. The SLR7RMMOM can switch from one operation mode to another without disconnection and reassembly, and is a non-overconstrained mechanism. The algorithm for the inverse kinematics of the serial 6R mechanism using kinematic mapping is adopted to deal with the kinematic analysis of the SLR7RMMOM. First, a numerical method is applied and an example is given to show that there are 13 sets of solutions for the SLR7RMMOM, corresponding to each input angle. Among these solutions, nine sets are real solutions, which are verified using both a computer-aided design (CAD) model and a prototype of the mechanism. Then an algebraic approach is also used to analyse the mechanism and same results are obtained as the numerical one. It is shown from both numerical and algebraic approaches that the SLR7RMMOM has three operation modes: a translational mode and two 1-DOF planar modes. The transitional configurations among the three modes are also identified.

Architecture Optmization of a 3-DOF Parallel Mechanism

1998 ◽  
Author(s):  
J. A. Carretero ◽  
R. P. Podhorodeski ◽  
M. Nahon
Keyword(s):  
Parallel Mechanism ◽  
Architectural Design ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Design Parameters ◽  
Objective Functions ◽  
Constraint Equations ◽  
Three Degree Of Freedom ◽  
Architecture Optimization ◽  
Three Degrees Of Freedom

Abstract This paper presents a study of the architecture optimization of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described. Since the mechanism has only three degrees of freedom, constraint equations describing the inter-relationship between the six Cartesian coordinates are given. These constraints allow us to define the parasitic motions and, if incorporated into the kinematics model, a constrained Jacobian matrix can be obtained. This Jacobian matrix is then used to define a dexterity measure. The parasitic motions and dexterity are then used as objective functions for the optimizations routines and from which the optimal architectural design parameters are obtained.

scholarly journals Influence of design parameters on the singularities and workspace of a 3-RPS parallel robot

2018 ◽  
Vol 42 (1) ◽  
pp. 30-37 ◽  
Author(s):  
Ranjan Jha ◽  
Damien Chablat ◽  
Luc Baron
Keyword(s):  
Design Parameter ◽  
Parallel Manipulator ◽  
Decomposition Method ◽  
Parallel Robot ◽  
Joint Space ◽  
Mobile Platform ◽  
Design Parameters ◽  
Cylindrical Algebraic Decomposition ◽  
Parasitic Motion

This paper presents variations in the workspace, singularities, and joint space with respect to design parameter k, which is the ratio of the dimensions of the mobile platform to the dimensions of the base of a 3-RPS parallel manipulator. The influence of the design parameters on parasitic motion, which is important when selecting a manipulator for a desired task, is also studied. The cylindrical algebraic decomposition method and Gröbner-based computations are used to model the workspace and joint space with parallel singularities in 2R1T (two rotational and one translational) and 3T (three translational) projection spaces, where the orientation of the mobile platform is represented using quaternions. These computations are useful in selecting the optimum value for the design parameter k such that the parasitic motions can be limited to specific values. Three designs of the 3-RPS parallel robot, based on different values of k, are analyzed.

Task-based torque minimization of a 3-PṞR spherical parallel manipulator

Robotica ◽  
2021 ◽  
pp. 1-30
Author(s):  
Soheil Zarkandi
Keyword(s):  
Closed Form ◽  
Dynamic Modeling ◽  
Dynamic Equation ◽  
Parallel Manipulator ◽  
Optimization Problem ◽  
Dynamic Constraints ◽  
Part C ◽  
Euler Approach ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

Abstract A comprehensive dynamic modeling and actuator torque minimization of a new symmetrical three-degree-of-freedom (3-DOF) 3-PṞR spherical parallel manipulator (SPM) is presented. Three actuating systems, each of which composed of an electromotor, a gearbox and a double Rzeppa-type driveshaft, produce input torques of the manipulator. Kinematics of the 3-PṞR SPM was recently studied by the author (Zarkandi, Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci. 2020, https://doi.org/10.1177%2F0954406220938806). In this paper, a closed-form dynamic equation of the manipulator is derived with the Newton–Euler approach. Then, an optimization problem with kinematic and dynamic constraints is presented to minimize torques of the actuators for implementing a given task. The results are also verified by the SimMechanics model of the manipulator.

Integrated Kinematic Calibration for All the Parameters of a Planar 2DOF Redundantly Actuated Parallel Manipulator

2009 ◽  
Vol 1 (3) ◽  
Author(s):  
Chunshi Feng ◽  
Shuang Cong ◽  
Weiwei Shang
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Open Loop ◽  
Kinematic Calibration ◽  
Constraint Equations ◽  
Integrated Method ◽  
Uniqueness Of The Solution ◽  
Redundantly Actuated ◽  
Loop Constraint ◽  
Two Degree Of Freedom

In this paper, the kinematic calibration of a planar two-degree-of-freedom redundantly actuated parallel manipulator is studied without any assumption on parameters. A cost function based on closed-loop constraint equations is first formulated. Using plane geometry theory, we analyze the pose transformations that bring infinite solutions and present a kinematic calibration integrated of closed-loop and open-loop methods. In the integrated method, the closed-loop calibration solves all the solutions that fit the constraint equations, and the open-loop calibration guarantees the uniqueness of the solution. In the experiments, differential evolution is applied to compute the solution set, for its advantages in computing multi-optima. Experimental results show that all the parameters involved are calibrated with high accuracy.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

The Optimum Kinematic Design of a Spherical Three-Degree-of-Freedom Parallel Manipulator

1989 ◽  
Vol 111 (2) ◽  
pp. 202-207 ◽  
Author(s):  
C. Gosselin ◽  
J. Angeles
Keyword(s):  
Numerical Method ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Design Criteria ◽  
Kinematic Design ◽  
Three Degree Of Freedom

In this paper, the design of a spherical three-degree-of-freedom parallel manipulator is considered from a kinematic viewpoint. Three different design criteria are established and used to produce designs having optimum characteristics. These criteria are (a) symmetry (b) workspace maximization, and (c) isotropy. The associated problems are formulated and their solutions, one of them requiring to resort to a numerical method, are provided. Optimum designs are thereby obtained. A discussion on singularities is also included.

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