Kinematics of the (nS)-2SPU Wrist

2011 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Design Stage ◽  
Control Algorithms ◽  
End Effector ◽  
Singular Configurations

The majority of the manipulation tasks requires the motion of the end effector from an initial pose to a final one without particular conditions on the path. Thus, the reduction of the practicable paths between two any poses is a possible choice, exploitable at the design stage, for simplifying manipulator’s hardware. This choice is adopted in under-actuated manipulators. The (nS)-2SPU wrist is one out of the under-actuated parallel wrists this author proposed in a previous paper. Here, the kinematic analysis of this wrist is studied. Both its finite and its elementary kinematics are considered. It is shown that its control algorithms can be written by using simple closed-form formulas, which can take advantage from the wide literature on spherical four-bar linkages. And the demonstration that its singular configurations can be avoided more easily than the ones of the fully-parallel wrist is provided.

Kinematic Analysis of the (nS)-2SPU Underactuated Parallel Wrist

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Design Stage ◽  
Control Algorithms ◽  
End Effector ◽  
Singular Configurations ◽  
Underactuated Manipulators

The majority of the manipulation tasks require the motion of the end-effector from an initial pose to a final one without any particular condition on the path. Thus, the reduction of the practicable paths between any two poses is a possible choice, exploitable at the design stage, for simplifying the manipulator hardware. This choice is adopted in underactuated manipulators. The (nS)-2SPU wrist is one out of the underactuated parallel wrists this author proposed in a previous paper. Here, the kinematic analysis of this wrist is studied: both its finite and its elementary kinematics are considered. It is shown that its control algorithms can be written by using simple closed-form formulas, which can take advantage from the wide literature on the spherical four-bar linkages. Moreover, the demonstration that its singular configurations can be avoided more easily than the ones of the fully parallel wrist is provided.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Vol 129 (6) ◽  
pp. 611-616 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Clément M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schönflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

A new parallel wrist using only revolute pairs: the 3-RUU wrist

Robotica ◽  
2001 ◽  
Vol 19 (3) ◽  
pp. 305-309 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Explicit Form ◽  
Kinematic Analysis ◽  
Degrees Of Freedom ◽  
Geometric Errors ◽  
End Effector ◽  
Singular Configurations ◽  
Overconstrained Mechanisms ◽  
Three Degrees Of Freedom

Only one parallel wrist with three equal legs containing just revolute pairs has been already presented in the literature. This parallel wrist is overconstrained, i.e., it involves three degrees of freedom required to orientate the end effector by using repetitions of constraints. The overconstrained mechanisms have the drawback of jamming or undergoing high internal loads when geometric errors occur. This paper presents a new parallel wrist, named 3-RUU wrist. The 3-RUU wrist is not overconstrained. It has three equal legs just involving revolute pairs and actuators adjacent to the frame and uses an architecture (3-RUU) already employed to obtain manipulators that make the end effector translate. The 3-RUU wrist kinematic analysis is addressed. This analysis shows that the new parallel wrist can reach singular configurations (translation singularities) in which the spherical constraint between end effector and frame fails. The singularity condition that makes finding all the 3-RUU wrist singular configurations possible is written in explicit form and geometrically interpreted.

Kinematic Analysis and Prototyping of a Partially Decoupled 4-DOF 3T1R Parallel Manipulator

2006 ◽  
Author(s):  
Pierre-Luc Richard ◽  
Cle´ment M. Gosselin ◽  
Xianwen Kong
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Quadratic Equation ◽  
Design Stage ◽  
Forward Displacement ◽  
Singular Configurations ◽  
The Family ◽  
Moving Platform ◽  
Forward Displacement Analysis

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Scho¨nflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are: (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently.

scholarly journals Sensitivity Analysis of the Orthoglide, a 3-DOF Translational Parallel Kinematic Machine

2004 ◽  
Author(s):  
Ste´phane Caro ◽  
Philippe Wenger ◽  
Fouad Bennis ◽  
Damien Chablat
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Analysis ◽  
Design Parameters ◽  
Analysis Method ◽  
Parallel Kinematic Machine ◽  
Vector Method ◽  
End Effector ◽  
Singular Configurations ◽  
Parallel Kinematic ◽  
Position And Orientation

This paper presents a sensitivity analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. Two complementary methods are used to analyze its sensitivity to its dimensional and angular variations. First, a linkage kinematic analysis method is used to have a rough idea of the influence of the dimensional variations on the location of the end-effector, and shows that the variations in design parameters of the same type from one leg to another one have the same influence on the end-effector. However, this method does not allow the designer to know the influence of the variations in the parallelograms. Thus, a differential vector method is used to study the influence of the dimensional and angular variations in the parts of the manipulator, and particularly the variations in the parallelograms, on the position and orientation of the end-effector. It turns out that the isotropic kinematic configuration of the manipulator is the least sensitive one to its geometrical variations, contrary to the closest configurations to its kinematic singular configurations, which are the most sensitive to geometrical variations.

Singularity Analysis of 2-DOF Parallel Manipulator

2012 ◽  
Vol 569 ◽  
pp. 589-592
Author(s):  
Jong Gyu Lee ◽  
Sang Ryong Lee ◽  
Choon Young Lee ◽  
Seung Han Yang
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Strong Influence ◽  
Orientation Angle ◽  
Singularity Analysis ◽  
End Effector ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Workspace Boundary

The end-effector of 2-DOF parallel manipulator has an orientation. Jacobian matrices are obtained by kinematic analysis. The singular configurations of the manipulator are found using these matrices and the certain characteristic of these configurations is investigated. With the result from simulation, we found that these configurations happened to workspace-interior as well as workspace-boundary and the orientation angle of the end-effector exerted a strong influence on the singularity of the manipulator.

A Parallelogram-Based Parallel Manipulator For Scho¨nflies Motion

2006 ◽  
Author(s):  
Oscar Salgado ◽  
Oscar Altuzarra ◽  
Enrique Amezua ◽  
Alfonso Herna´ndez
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Singularity Analysis ◽  
End Effector ◽  
Fixed Direction ◽  
Axis Parallel

A parallelogram-based four degrees-of-freedom parallel manipulator is presented in this paper. The manipulator can generate the so-called Scho¨nflies motion, that allows the end-effector to translate in all directions and rotate around an axis parallel to a fixed direction. The Theory of Group of Displacements is applied in the synthesis of this manipulator, which employs parallelograms in every limb. The planar parallelogram kinematic chain provides a high rotational capability and a improved stiffness to the manipulator. The paper shows the kinematic analysis of the manipulator, including the closed-form resolution of the forward and inverse position problems, the velocity and the singularity analysis. Finally, a prototype of the manipulator and some technical applications in which the manipulator can be used are presented.

scholarly journals Differential Kinematics Of Contemporary Industrial Robots

2014 ◽  
Vol 19 (3) ◽  
pp. 643-659
Author(s):  
T. Szkodny
Keyword(s):  
Closed Form ◽  
Robot Manipulators ◽  
Industrial Robot ◽  
Industrial Robots ◽  
The Other ◽  
Simple Method ◽  
End Effector ◽  
Singular Configurations ◽  
Global Form

Abstract The paper presents a simple method of avoiding singular configurations of contemporary industrial robot manipulators of such renowned companies as ABB, Fanuc, Mitsubishi, Adept, Kawasaki, COMAU and KUKA. To determine the singular configurations of these manipulators a global form of description of the end-effector kinematics was prepared, relative to the other links. On the basis of this description , the formula for the Jacobian was defined in the end-effector coordinates. Next, a closed form of the determinant of the Jacobian was derived. From the formula, singular configurations, where the determinant’s value equals zero, were determined. Additionally, geometric interpretations of these configurations were given and they were illustrated. For the exemplary manipulator, small corrections of joint variables preventing the reduction of the Jacobian order were suggested. An analysis of positional errors, caused by these corrections, was presented

Delta robot: Inverse, direct, and intermediate Jacobians

2006 ◽  
Vol 220 (1) ◽  
pp. 103-109 ◽  
Author(s):  
M López ◽  
E Castillo ◽  
G García ◽  
A Bashir
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Kinematic Chain ◽  
End Effector ◽  
Jacobian Matrices ◽  
Singular Configurations ◽  
Delta Robot ◽  
Intermediate Jacobian

In the context of a parallel manipulator, inverse and direct Jacobian matrices are known to contain information which helps us identify some of the singular configurations. In this article, we employ kinematic analysis for the Delta robot to derive the velocity of the end-effector in terms of the angular joint velocities, thus yielding the Jacobian matrices. Setting their determinants to zero, several undesirable postures of the manipulator have been extracted. The analysis of the inverse Jacobian matrix reveals that singularities are encountered when the limbs belonging to the same kinematic chain lie in a plane. Two of the possible configurations which correspond to this condition are when the robot is completely extended or contracted, indicating the boundaries of the workspace. Singularities associated with the direct Jacobian matrix, which correspond to relatively more complicated configurations of the manipulator, have also been derived and commented on. Moreover, the idea of intermediate Jacobian matrices have been introduced that are simpler to evaluate but still contain the information of the singularities mentioned earlier in addition to architectural singularities not contemplated in conventional Jacobians.

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