Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

Kinematic Synthesis of a Spatial 3-RPS Parallel Manipulator

2003 ◽  
Vol 125 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Han Sung Kim ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Point Of View ◽  
Dimensional Synthesis ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Solution Methods ◽  
Moving Platform ◽  
At Will

This paper presents the design of spatial 3-RPS parallel manipulators from dimensional synthesis point of view. Since a spatial 3-RPS manipulator has only 3 degrees of freedom, its end effector cannot be positioned arbitrarily in space. It is shown that at most six positions and orientations of the moving platform can be prescribed at will and, given six prescribed positions, there are at most ten RPS chains that can be used to construct up to 120 manipulators. Further, solution methods for fewer than six prescribed positions are also described.

Dimensionally Homogeneous Jacobian and Condition Number

2016 ◽  
Vol 836 ◽  
pp. 42-47 ◽  
Author(s):  
Latifah Nurahmi ◽  
Stéphane Caro
Keyword(s):  
Performance Analysis ◽  
Condition Number ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Moving Platform ◽  
Conditioning Number

This paper deals with the formulation of the dimensionally homogeneous extended Jacobian matrix, which is an important issue for the performance analysis of f degrees-of-freedom (f ≤6) parallel manipulators having coupled rotational and translational motions. By using the f independent coordinates to define the permitted motions and (6-f) independent coordinates to define the restricted motions of the moving platform, the 6×6 dimensionally homogeneous extended Jacobian matrix is derived for non-redundant parallel manipulators. The conditioning number of the parallel manipulators is computed to evaluate the homogeneous extended Jacobian matrix, the homogeneous actuation wrench matrix, and the homogeneous constraint wrench matrix to evaluate the performance of the parallel manipulators. By using these indices, the closeness of a pose to different singularities can be detected. An illustrative example with the 3-RPS parallel manipulator is provided to highlight the effectiveness of the approach and the proposed indices.

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

A novel class of generalized parallel manipulators with high rotational capability

2020 ◽  
Vol 234 (23) ◽  
pp. 4599-4619
Author(s):  
Chunxu Tian ◽  
Dan Zhang ◽  
Jian Liu
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Kinematic Chains ◽  
Moving Platforms ◽  
Moving Platform ◽  
Limb Structure

A conventional parallel manipulator is characterized by connecting one moving platform with two or more serial kinematic limbs. Since each limb is independently supporting one moving platform, the moving platform must be a rigid body with several kinematic pairs fixed on it. However, for generalized parallel manipulators with articulated moving platforms, the moving platforms are not limited to rigid bodies but including serial kinematic chains or internal kinematic joints. The introduction of articulated moving platforms allows for improving the kinematic performance of generalized parallel manipulators, especially for rotational capability. On account of the structural characteristics of the moving platforms, it also poses a significant challenge in the construction of the structures of manipulators. This research raises a new method for the type synthesis of generalized parallel manipulators with novel articulated moving platforms. The proposed method introduces a striking shortcut for the limb structure analysis of mechanisms with high rotational capability. In this paper, a class of generalized parallel manipulator with different degrees of freedom from 3 to 6 are constructed by using the constraint synthesis method, and several examples are provided to demonstrate the feasibility of the advocated method. At last, the 3T3R generalized parallel manipulator is taken as an example to analyze the inverse kinematics, and the evaluation of the workspace is conducted to verify the rotational capacity.

Sensitivity Analysis of Planar Parallel Manipulators

2008 ◽  
Author(s):  
Ste´phane Caro ◽  
Nicolas Binaud ◽  
Philippe Wenger
Keyword(s):  
Sensitivity Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Sensitivity Coefficients ◽  
Planar Parallel Manipulator ◽  
Moving Platform ◽  
Conditioning Number ◽  
Planar Parallel Manipulators

This paper deals with the sensitivity analysis of planar parallel manipulators. A methodology is introduced to derive the sensitivity coefficients by means of the study of 3-RPR manipulators. As a matter of fact, the sensitivity coefficients of the pose of its moving platform to variations in the geometric parameters are expressed algebraically, the variations being defined both in Polar and Cartesian coordinates. The dexterity of the manipulator is also studied by means of the conditioning number of its normalized kinematic Jacobian matrix. As an illustrative example, the sensitivity of a symmetrical planar parallel manipulator is analyzed in detail. Finally, the accuracy of the manipulator is compared with its dexterity.

Direct Singular Positions of 3RPS Parallel Manipulators

2004 ◽  
Vol 126 (6) ◽  
pp. 1006-1016 ◽  
Author(s):  
C. H. Liu ◽  
Shengchia Cheng
Keyword(s):  
Circular Cylinder ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Second Step ◽  
Horizontal Position ◽  
Solid Cylinder ◽  
Singular Configurations ◽  
Solid Circular Cylinder ◽  
Moving Platform

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of three spherical joints, denoted by d1n,d2n, and d3n respectively, are used as coordinate axes, then the workspace of the moving platform may be represented as an inclined solid cylinder in this coordinate system. The location of a point on the solid circular cylinder determines a configuration of the manipulator’s moving platform. The procedure to locate direct singular positions consists of two steps, the orientation of the moving platform is assumed first, from which the horizontal position of the moving platform may be obtained. Then in the second step the heights that make determinant of the Jacobian matrix vanish may always be determined. Results show that unless the moving platform is normal to the base, in which case there exist only one or two singular configurations, otherwise there are always three singular configurations corresponding to a moving platform’s orientation.

Jacobian Analysis of Limited-DOF Parallel Manipulators

2002 ◽  
Vol 124 (2) ◽  
pp. 254-258 ◽  
Author(s):  
Sameer A. Joshi ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Six Degrees Of Freedom

This paper presents a methodology for the Jacobian analysis of limited degrees-of-freedom (DOF) parallel manipulators. A limited-DOF parallel manipulator is a spatial parallel manipulator which has less than six degrees-of-freedom. It is shown that a 6×6 Jacobian matrix, which provides information about both architecture and constraint singularities, can be derived by making use of the theory of reciprocal screws. The 3-UPU and 3-RPS parallel manipulators are used as examples to demonstrate the methodology.

Direct Singular Positions of 3RPS Parallel Manipulators

2004 ◽  
Author(s):  
C. H. Liu ◽  
Shengchia Cheng
Keyword(s):  
Circular Cylinder ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Second Step ◽  
Horizontal Position ◽  
Solid Cylinder ◽  
Singular Configurations ◽  
Solid Circular Cylinder ◽  
Moving Platform

In this study a procedure to obtain direct singular positions of a 3RPS parallel manipulator is presented. If the heights of 3 spherical joints, denoted by d1n, d2n, and d3n respectively, are used as coordinate axes, then the workspace of the moving platform may be represented as an inclined solid cylinder in this coordinate system. The location of a point on the solid circular cylinder determines a configuration of the manipulator’s moving platform. The procedure to locate direct singular positions consists of two steps, the orientation of the moving platform is assumed first, from which the horizontal position of the moving platform may be obtained; then in the second step the heights that make determinant of Jacobian matrix vanish may always be determined. Results show that unless the moving platform is normal to the base, in which case there exist only one or two singular configurations, otherwise there are always three singular configurations corresponding to a moving platform’s orientation.

Kinematics of a Particular 3T1R Parallel Manipulator of Type 2PRPU

2017 ◽  
Author(s):  
Henrique Simas ◽  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
End Effector ◽  
Serial Robots ◽  
Fixed Direction ◽  
Pick And Place ◽  
Displacement Group ◽  
4 Degrees Of Freedom

Schoenflies-motion generators (SMGs) are 4-degrees-of-freedom (dof) manipulators whose end effector can perform translations along three independent directions, and rotations around one fixed direction (Schoenflies motions). Such motions constitute the 4-dimensional (4-D) Schoenflies subgroup of the 6-D displacement group. The most known SMGs are the serial robots named SCARA. Pick-and-place tasks are typical industrial applications that SMGs can accomplish. In the literature, 3T1R parallel manipulators (PMs) have been also proposed as SMGs. Here, a somehow novel 3T1R PM is presented and studied. Its finite and instantaneous kinematics are analyzed in depth, and analytic and geometric tools that are useful for its design are presented. The proposed SMG has a single-loop not-overconstrained architecture with actuators on or near the base and can make the end effector perform a complete rotation.

scholarly journals SINGULARITY ANALYSIS OF THE 4 RUU PARALLEL MANIPULATOR USING GRASSMANN-CAYLEY ALGEBRA

2011 ◽  
Vol 35 (4) ◽  
pp. 515-528 ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Fixed Direction ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of four degrees of freedom parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction. The 6 × 6 Jacobian matrix of such manipulators contains two lines at infinity among its six Plücker vectors. Some points at infinity are thus introduced to formulate the superbracket of Grassmann-Cayley algebra, which corresponds to the determinant of the Jacobian matrix. By exploring this superbracket, all the singularity conditions of such manipulators can be enumerated. The study is illustrated through the singularity analysis of the 4-RUU parallel manipulator.

Sign in / Sign up

Export Citation Format

Share Document