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 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 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.

An inverse position analysis of five-bar planar parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (2) ◽  
pp. 195-201 ◽  
Author(s):  
Gürsel Alici
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Computationally Efficient ◽  
Simple Method ◽  
Cartesian Coordinates ◽  
Reachable Workspace ◽  
Prismatic Joints ◽  
Inverse Position Analysis ◽  
Translational Joint ◽  
Planar Parallel Manipulators

In this paper, we present a simple method to obtain joint inputs needed to attain any point in the reachable workspace of a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. Depending on the topology of the manipulators, two mathematical expressions describing the path traced by the tip of two links connected to each other are obtained and solved simultaneously in order to determine the intersection points of the two paths which are the Cartesian coordinates of the connection points for the links. For the class of manipulators considered in this study, one of the links is the link activated by an actuator fixed to the ground. So, rotational and/or translational joint inputs can be determined from the Cartesian coordinates of the tip of the activated links. Sylvester's dialytic elimination method is employed to solve the equations. Such a methodology is easy to implement, computationally efficient and sound to compute all possible solutions. A numerical example is provided for each manipulator and the inverse position solutions are verified by substituting them into forward position equations. It is concluded that the proposed method is useful in trajectory planning and control of five-bar planar parallel manipulators in joint space.

Planar Linkage Synthesis for Mixed Exact and Approximated Motion Realization Via Kinematic Mapping

2016 ◽  
Vol 8 (5) ◽  
Author(s):  
Ping Zhao ◽  
Xin Ge ◽  
Bin Zi ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Parallel Manipulators ◽  
Surface Fitting ◽  
Dimensional Synthesis ◽  
Constraint Equations ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
Mapping Theory ◽  
Discrete Motion ◽  
Fitting Problem

It has been well established that kinematic mapping theory could be applied to mechanism synthesis, where discrete motion approximation problem could be converted to a surface fitting problem for a group of discrete points in hyperspace. In this paper, we applied kinematic mapping theory to planar discrete motion synthesis of an arbitrary number of approximated poses as well as up to four exact poses. A simultaneous type and dimensional synthesis approach is presented, aiming at the problem of mixed exact and approximate motion realization with three types of planar dyad chains (RR, RP, and PR). A two-step unified strategy is established: first N given approximated poses are utilized to formulate a general quadratic surface fitting problem in hyperspace, then up to four exact poses could be imposed as pose-constraint equations to this surface fitting system such that they could be strictly satisfied. The former step, the surface fitting problem, is converted to a linear system with two quadratic constraint equations, which could be solved by a null-space analysis technique. On the other hand, the given exact poses in the latter step are formulated as linear pose-constraint equations and added back to the system, where both type and dimensions of the resulting optimal dyads could be determined by the solution. These optimal dyads could then be implemented as different types of four-bar linkages or parallel manipulators. The result is a novel algorithm that is simple and efficient, which allows for N-pose motion approximation of planar dyads containing both revolute and prismatic joints, as well as handling of up to four prescribed poses to be realized precisely.

Determination of singularity contours for five-bar planar parallel manipulators

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 569-575 ◽  
Author(s):  
Gürsel Alıcı
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Point Of View ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Singular Configurations ◽  
Planning And Design ◽  
Prismatic Joints ◽  
Planar Parallel Manipulators

From a design point of view, it is crucial to predict singular configurations of a manipulator in terms of inputs in order to improve the dexterity and workspace of a manipulator. In this paper, we present a simple, yet a systematic appoach to obtain singularity contours for a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. The determinants of the manipulator Jacobian matrices are evaluated in terms of joint inputs for a specified set of geometric parameters, and the contours of the determinants at 0.0 plane which are the singularity contours in joint space are generated for the three types of singularities reported in the literature. The proposed approach/algorithm is simple and systematic, and the resulting equations are easy to solve on a computer. The singularity contours for all the class are presented in order to demonstrate the method. It is concluded that the proposed method is useful in trajectory planning and design of five-bar planar parallel manipulators in order to improve their dexterity and workspace.

Planar Linkage Synthesis for Mixed Exact and Approximated Motion Realization via Kinematic Mapping

2015 ◽  
Author(s):  
Ping Zhao ◽  
Xin Ge ◽  
Bin Zi ◽  
Q. J. Ge
Keyword(s):  
Null Space ◽  
Parallel Manipulators ◽  
Surface Fitting ◽  
Realization Problem ◽  
Constraint Equations ◽  
Kinematic Mapping ◽  
Motion Approximation ◽  
Mapping Theory ◽  
Discrete Motion ◽  
Fitting Problem

It has been well established that kinematic mapping theory could be applied in mechanism synthesis area, where discrete motion approximation problem could be converted to surface fitting problem of a group of discrete points in hyperspace. In this paper, we applied kinematic mapping theory to planar discrete motion synthesis of an arbitrary number of approximated poses as well as up to four exact poses. A simultaneous type and dimensional synthesis approach for mixed exact and approximate motion realization problem for three types of planar dyad chains (RR, RP, PR) is presented. For all three types of dyads, N given approximated poses are utilized to formulate a general quadratic surface fitting problem in hyperspace, while up to four prescribed poses could be imposed as pose-constraint equations to this surface fitting system such that they could be exactly realized. The surface fitting problem is converted to a linear system with two quadratic constraint equations, which could be solved by null space analysis technique. On the other hand, the given exact poses are formulated as linear pose-constraint equations and added back to the system, where both type and dimensions of the resulting optimal dyads could be determined by the solution. These optimal dyads could then be implemented as different types of four-bar linkages or parallel manipulators. The result is a novel algorithm that is simple and efficient, which allows for N-pose motion approximation of planar dyads containing both revolute and prismatic joints, as well as handling of up to four prescribed poses to be realized precisely.

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 Regions of Feasible Point-to-Point Trajectories in the Cartesian Workspace of Fully-Parallel Manipulators

1999 ◽  
Author(s):  
Damien Chablat ◽  
Philippe Wenger
Keyword(s):  
Parallel Manipulator ◽  
Cartesian Product ◽  
Parallel Manipulators ◽  
Joint Space ◽  
Inverse Kinematic ◽  
Connected Components ◽  
Feasible Point ◽  
Cartesian Space ◽  
Point Trajectories ◽  
Point To Point

Abstract The goal of this paper is to define the n-connected regions in the Cartesian workspace of fully-parallel manipulators, i.e. the maximal regions where it is possible to execute point-to-point motions. The manipulators considered in this study may have multiple direct and inverse kinematic solutions. The N-connected regions are characterized by projection, onto the Cartesian workspace, of the connected components of the reachable configuration space defined in the Cartesian product of the Cartesian space by the joint space. Generalized octree models are used for the construction of all spaces. This study is illustrated with a simple planar fully-parallel manipulator.

Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 791-802 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Linear Mapping ◽  
Redundant Manipulators ◽  
Task Space ◽  
Performance Indices ◽  
Study Case ◽  
And Performance ◽  
Planar Parallel Manipulators

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

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