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 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 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 Optimal Design of a 3-DOF Cable-Driven Upper Arm Exoskeleton

2014 ◽  
Vol 6 ◽  
pp. 157096 ◽  
Author(s):  
Zhu-Feng Shao ◽  
Xiaoqiang Tang ◽  
Wangmin Yi
Keyword(s):  
Optimal Design ◽  
Working Conditions ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Design Parameters ◽  
Rehabilitation Robot ◽  
Challenging Problem ◽  
System Safety ◽  
Upper Arm ◽  
Global Force

With outstanding advantages, such as large workspace, flexibility, and lightweight and low inertia, cable-driven parallel manipulator shows great potential for application as the exoskeleton rehabilitation robot. However, the optimal design is still a challenging problem to be solved. In this paper, the optimal design of a 3-DOF (3-degree-of-freedom) cable-driven upper arm exoskeleton is accomplished considering the force exerted on the arm. After analysis of the working conditions, two promising configurations of the cable-driven upper arm exoskeleton are put forward and design parameters are simplified. Then, candidate ranges of two angle parameters are determined with the proposed main workspace requirement. Further, global force indices are defined to evaluate the force applied to the arm by the exoskeleton, in order to enhance the system safety and comfort. Finally, the optimal design of each configuration is obtained with proposed force indices. In addition, atlases and charts given in this paper well illustrate trends of workspace and force with different values of design parameters.

scholarly journals Kinematic Analysis Of Tricept Parallel Manipulator

2012 ◽  
Vol 12 (5) ◽  
Author(s):  
Mir Amin Hosseini ◽  
Hamid-Reza Mohammadi Daniali
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometric Constraints ◽  
Design Parameters ◽  
Forward Kinematics ◽  
Jacobian Matrices ◽  
Moving Platforms ◽  
Workspace Optimization

Parallel manipulators consist of fixed and moving platforms connected to each other with some actuated links. They have some significant advantages over their serial counterparts. While, they suffer from relatively small workspaces, complex kinematics relations and highly singular points within their workspaces. In this paper, forward kinematics of Tricept parallel manipulator is solved analytically and its workspace optimization is performed. This parallel manipulator has a complex degree of freedom, therefore leads to dimensional in-homogeneous Jacobian matrices. Thus, we divide some entries of the Jacobian by units of length, thereby producing a new Jacobian that is dimensionally homogeneous. Moreover, its workspace is parameterized using some design parameters. Then, using GA method, the workspace is optimized subjects to some geometric constraints. Finally, dexterity of the design is evaluated. Keywords- Kinematic, Workspace, Singularity, TriceptABSTRAK - Manipulator selari terdiri daripada platform tetap dan bergerak yang bersambung antara satu sama lain dengan beberapa pautan bergerak. Manipulator selari mempunyai beberapa kebaikan tertentu dibandingkan dengan yang bersamaan dengannya. Walaupun ia mempunyai ruang kerja yang sempit, hubungan kinematik kompleks dan titik tunggal tinggi dalam linkungan ruang kerjanya. Dalam kajian ini, kinematik ke hadapan manipulator selari Tricept diselesaikan secara analisa dan pengoptimuman ruang kerja dijalankan. Manipulator selari ini mempunyai darjah kebebasan yang kompleks, yang menyebabkan ia mendorong kepada kehomogenan dimensi matriks Jacobian. Catatan Jacobian dibahagikan kepada unit panjang, dimana ia menghasilkan Jacobian baru yang homogen dimensinya. Tambahan, ruang kerjanya diparameterkan dengan menggunakan beberapa parameter reka bentuk. Kemudian, dengan kaedah GA, ruang kerja mengoptimakan subjek kepada beberapa kekangan geometrik. Akhirnya, kecakatan reka bentuk dinilaikan.Keywords- Kinematic, Workspace, Singularity, Tricept

Reconfiguration of a 3-(rR)PS Metamorphic Parallel Mechanism Based on Complete Workspace and Operation Mode Analysis

2019 ◽  
Vol 12 (1) ◽  
Author(s):  
Latifah Nurahmi ◽  
Dongming Gan
Keyword(s):  
Parallel Mechanism ◽  
Operation Mode ◽  
Mode Analysis ◽  
Finite Point ◽  
Constraint Equations ◽  
Revolute Joints ◽  
Operation Modes ◽  
Identification Approach ◽  
Moving Platform ◽  
Mode A

Abstract This paper focuses on the reconfiguration of a 3-(rR)PS metamorphic parallel mechanism based on complete workspace and operation mode analysis. The mechanism consists of three (rR)PS legs, and each (rR) joint is composed of two perpendicular revolute joints. One of the (rR) joint axes can be reconfigured continuously, which allows the mechanism to exhibit three distinct configurations. Initially, the constraint equations are derived by using algebraic geometry approach, and the primary decomposition is computed for the three configurations. It reveals that the 3-(rR)PS metamorphic parallel mechanism can exhibit one up to two operation modes among three configurations. When the second axes of the three (rR) joints intersect at a finite point and not coplanar, the 3-(rR)PS metamorphic parallel mechanism has only one operation mode. If the second axes of the three (rR) joints are coplanar, the 3-(rR)PS metamorphic parallel mechanism has two operation modes. It is shown that both operation modes have the same motion type, namely, 1T2R motion. However, to realize the same trajectories in both operation modes, the moving platform will have different orientations. Hence, the orientation workspaces of both operation modes are characterized and the axodes are used to compare the instantaneous motion of the moving platform when passing through the same trajectories. Based on these results, an identification approach is introduced to identify which operation mode a given mechanism pose belongs to and this provides a useful method for trajectory planning.

scholarly journals Kinematics Simulation of Gough-Stewart Parallel Manipulator by Using Simulink Package in Matlab Software

2019 ◽  
Vol 27 (2) ◽  
pp. 10-20
Author(s):  
Hassan Mohammed Alwan ◽  
Riyadh Ahmed Sarhan
Keyword(s):  
Theoretical Model ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Matlab Software ◽  
Kinematics Simulation ◽  
Moving Platform ◽  
Position And Orientation ◽  
Six Degree Of Freedom ◽  
Forward Equations

The Gough Stewart Robotic manipulator is a parallel manipulator with six-degree of freedom, which has six equations of Kinematics (Inverse and forward), with six variables (Lengths, Position, and Orientation). In this work derived the inverse equations, which used to compute the lengths of the linkages and its changes depended on the position and orientation of the platform's center, then derived the forward equations to calculate the position and orientation of the moving platform in terms of the lengths. This theoretical model of the kinematics analysis of the Gough Stewart has been built into the Simulink package in Matlab to obtain the lengths, position, and orientation for the manipulator at any time of motion. The input parameters (Position and Orientation) in inverse blocks compared with the output parameters (Position and Orientation) in the forward blocks, which show good results.

scholarly journals Design Procedure for a Fast and Accurate Parallel Manipulator

2017 ◽  
Vol 9 (6) ◽  
Author(s):  
Sébastien Briot ◽  
Stéphane Caro ◽  
Coralie Germain
Keyword(s):  
Parallel Manipulator ◽  
Dynamic Performance ◽  
Design Procedure ◽  
Design Parameters ◽  
Pick And Place ◽  
Static Performance ◽  
Moving Platform ◽  
Main Components ◽  
Two Degree Of Freedom ◽  
Very High

This paper presents a design procedure for a two degree-of-freedom (DOF) translational parallel manipulator, named IRSBot-2. This design procedure aims at determining the optimal design parameters of the IRSBot-2 such that the robot can reach a velocity equal to 6 m/s, an acceleration up to 20 G, and a multidirectional repeatability up to 20 μm throughout its operational workspace. Besides, contrary to its counterparts, the stiffness of the IRSBot-2 should be very high along the normal to the plane of motion of its moving platform. A semi-industrial prototype of the IRSBot-2 has been realized based on the obtained optimum design parameters. This prototype and its main components are described in the paper. Its accuracy, repeatability, elasto-static performance, dynamic performance, and elasto-dynamic performance have been measured and analyzed as well. It turns out that the IRSBot-2 has globally reached the prescribed specifications and is a good candidate to perform very fast and accurate pick-and-place operations.

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 Analysis of Finite Self Motion and Finite Dwell in Closed-Loop Mechanisms and Parallel Manipulators

2001 ◽  
Author(s):  
Sandipan Bandyopadhyay ◽  
Ashitava Ghosal
Keyword(s):  
Parallel Manipulator ◽  
Closed Loop ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Kinematic Constraints ◽  
Constraint Equations ◽  
First Order ◽  
Necessary And Sufficient Criteria ◽  
Necessary And Sufficient ◽  
Self Motion

Abstract In this paper, we present the necessary and sufficient criteria for finite self motion and finite dwell of the passive links of a parallel manipulator or a closed-loop mechanism. We study the first order properties of the constraint equations associated with the kinematic constraints inherent in a closed-loop mechanism or a parallel manipulator, and arrive at the criteria for the mechanism to gain a degree-of-freedom at a singular point of its workspace. By analyzing the second order properties of the constraint equations, we show that the gain of degree-of-freedom may lead to finite self motion of the passive links if certain configurational and architectural criteria are met. Special configurations and architecture may also lead to finite dwell of the passive links, and the criteria for the same has been derived. The results are illustrated with the help of several closed-loop mechanisms.

Stiffness Analysis of Inverted Tripod Parallel Manipulator

2017 ◽  
Vol 867 ◽  
pp. 205-211
Author(s):  
T. Geethapriyan ◽  
R. Manoj Samson ◽  
T. Muthuramalingam ◽  
A.C. Arun Raj
Keyword(s):  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Ball Screw ◽  
Stiffness Analysis ◽  
Adams Software ◽  
Movable Platform ◽  
Moving Platform ◽  
Rotation Motion ◽  
Three Degree Of Freedom ◽  
Stewart Gough Platform

The concept of parallel manipulator is becoming more popular in modern manufacturing processes due to its various inherent advantages like rigidity, less inertia and accuracy. This project focuses on modeling, simulation and dynamic analysis of inverted tripod parallel manipulator which has three degree of freedom (1 transverse in z axis and rotation motion in x and y axis). The Stewart Gough parallel manipulator consists of moving platform connected to fixed platform with six links (6 Degree of Freedom).This inverted tripod parallel manipulator consists of movable platform connected to the fixed platform with only three links so it has better rigidity compared to Stewart Gough platform. The Stewart Gough parallel manipulator is considered to be highly stable because moving platform size is smaller than the fixed platform. Inverted type parallel manipulator consists of moving platform bigger than the fixed platform. So to improve the stiffness and precision ball screw is used for the support of links. The design of parallel manipulator is done considering rigidity, strength and efficiency of the system. The modeling of the tripod manipulator is done using PRO-E software. Kinematic analysis has been carried out and the stiffness analysis will be done by using ANSYS and ADAMS software.

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