Forward Problem Singularities of Manipulators Which Become PS-2RS or 2PS-RS Structures When the Actuators Are Locked

2003 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Rigid Body ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Forward Problem ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (limbs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. This paper studies the singular geometries both of the PS-2RS structure and of the 2PS-RS structure. In particular, the singularity conditions of the two structures will be determined. Moreover, the geometric interpretation of their singularity conditions will be provided. Finally, the use of the obtained results in the design of parallel manipulators which become either PS-2RS or 2PS-RS structures, when the actuators are locked, will be illustrated.

Properties of the SX-YS-ZS Structures and Singularity Determination in Parallel Manipulators Which Generate Those Structures

2004 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Rigid Body ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Forward Problem ◽  
Unified Approach ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (legs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. In this paper, the singular geometries of the structures with topology SX-YS-ZS (S stands for spherical pair, whereas X, Y and Z stand for three generic one-dof pair which may be or may not be of the same type) are studied with a unified approach. The presented approach leads to obtain an analytic condition which allows all the singular geometries of these structures to be determined. Moreover, the geometric interpretation of the found singularity condition and the exhaustive enumeration of the types of singular geometries is provided. Finally, the use of the presented results in the design of the manipulators which become one structure with topology SX-YS-ZS when the actuators are locked is discussed.

Forward Problem Singularities of Manipulators Which Become PS-2RS or 2PS-RS Structures When the Actuators are Locked

2004 ◽  
Vol 126 (4) ◽  
pp. 640-645 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Rigid Body ◽  
Parallel Manipulators ◽  
Geometric Interpretation ◽  
Forward Problem ◽  
End Effector ◽  
Kinematic Chains ◽  
Geometric Conditions ◽  
New Form ◽  
Position And Orientation ◽  
Manipulator Design

The instantaneous forward problem (IFP) singularities of a parallel manipulator (PM) must be determined during the manipulator design and avoided during the manipulator operation, because they are configurations where the end-effector pose (position and orientation) cannot be controlled by acting on the actuators any longer, and the internal loads of some links become infinite. When the actuators are locked, PMs become structures consisting of one rigid body (platform) connected to another rigid body (base) by means of a number of kinematic chains (limbs). The geometries (singular geometries) of these structures where the platform can perform infinitesimal motion correspond to the IFP singularities of the PMs the structures derive from. This paper studies the singular geometries both of the PS-2RS structure and of the 2PS-RS structure. In particular, the singularity conditions of the two structures will be written in a new form. This new form will directly bring to a new geometric interpretation of their singularity conditions and to the exhaustive enumeration of the geometric conditions identifying their singular geometries. Such an enumeration will reveal that some geometric conditions were not identified in the literature. Finally, the use of the obtained results in the design of parallel manipulators which become either PS-2RS or 2PS-RS structures, when the actuators are locked, will be illustrated.

scholarly journals Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Alexey Fomin ◽  
Anton Antonov ◽  
Victor Glazunov ◽  
Yuri Rodionov
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Forward Kinematics ◽  
Rotational Angle ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design ◽  
Forward Kinematic

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

Accuracy Analysis of Parallel Manipulators With Joint Clearance

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
Jian Meng ◽  
Dongjun Zhang ◽  
Zexiang Li
Keyword(s):  
Parallel Manipulator ◽  
Optimization Problem ◽  
Parallel Manipulators ◽  
Joint Clearance ◽  
Error Prediction ◽  
Accuracy Analysis ◽  
Analysis Problem ◽  
Convex Optimization Problem ◽  
End Effector ◽  
Position And Orientation

Due to joint clearance, a parallel manipulator’s end-effector exhibits position and orientation (or collectively referred to as pose) errors of various degrees. This paper aims to provide a systematic study of the error analysis problem for a general parallel manipulator influenced by joint clearance. We propose an error prediction model that is applicable to planar or spatial parallel manipulators that are either overconstrained or nonoverconstrained. By formulating the problem as a standard convex optimization problem, the maximal pose error in a prescribed workspace can be efficiently computed. We present several numerical examples to show the applicability and the efficiency of the proposed method.

Evaluation of the Position Error of Four Non-Overconstrained Spherical Parallel Manipulators

2012 ◽  
Vol 162 ◽  
pp. 194-203
Author(s):  
A. Chaker ◽  
A. Mlika ◽  
M.A. Laribi ◽  
L. Romdhane ◽  
S. Zeghloul
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Position Error ◽  
Point Of View ◽  
Good Precision ◽  
End Effector ◽  
High Rigidity ◽  
Manufacturing Errors ◽  
Position And Orientation ◽  
Spherical Parallel Manipulator

The 3-RRR spherical parallel manipulator is known to be highly overconstrained, which causes several problems of mounting the mechanism, but has the advantage of having high rigidity thus a good precision. Several works in the literature proposed non-overconstrained versions of this mechanism. However, very few works dealt with the problem of the consequence of modifying an overconstrained mechanism into a non-overconstrained one, mainly from an accuracy point of view. In this work, we present an analysis of the accuracy of four different non-overconstrained SPMs, i.e., 3-RSR, 3-RCC, 3-RRS, and 3-RUU. These four SPM are then evaluated in translational and rotational accuracy due to manufacturing errors. The error on the position and orientation of the end-effector, due to manufacturing errors, are computed in 100 different configurations within their workspace. These SPMs are then compared among each other and we showed that the 3-RRS has the best compromise between the translational and rotational accuracy.

scholarly journals A Dexterity Comparison for 6 DOF Hybrid Robots

2020 ◽  
Author(s):  
MohammadAli Mohammadkhani ◽  
Ahmad Reza Haghighi
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
End Effector ◽  
Hybrid Mechanisms ◽  
Six Dof ◽  
Position And Orientation

Abstract In this paper, new hybrid robots are suggested which divided the task into a position and orientation tasks. The position mechanism controls the position whereas the orientation one manipulates the orientation of the end effector. These robots consist of a translational parallel manipulator and a rotational serial or parallel mechanism. The 3UPU or Tricept parallel manipulator and a three-axis gimbaled system or parallel shoulder manipulator are chosen for translational and rotational movements, respectively. The main goal of this paper is analyzing the development and combination of serial and parallel manipulators in order to increase their features. According to this purpose, serial and parallel mechanisms with three DOF are combined in a way to encompass six DOF space. It is shown hybrid mechanisms with less coupling between their subsystems are capable of increasing robot characteristics.

AN INTERVAL ANALYSIS METHOD FOR WRENCH WORKSPACE DETERMINATION OF PARALLEL MANIPULATOR ARCHITECTURES

2016 ◽  
Vol 40 (2) ◽  
pp. 139-154 ◽  
Author(s):  
Joshua K. Pickard ◽  
Juan A. Carretero
Keyword(s):  
Interval Analysis ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Design Parameters ◽  
End Effector ◽  
Interval Analysis Method ◽  
Reachable Workspace ◽  
Manipulator Design

This paper deals with the wrench workspace (WW) determination of parallel manipulators. The WW is the set of end-effector poses (positions and orientations) for which the active joints are able to balance a set of external wrenches acting at the end-effector. The determination of the WW is important when selecting an appropriate manipulator design since the size and shape of the WW are dependent on the manipulator’s geometry (design) and selected actuators. Algorithms for the determination of the reachable workspace and the WW are presented. The algorithms are applicable to manipulator architectures utilizing actuators with positive and negative limits on the force/torque they can generate, as well as cable-driven parallel manipulator architectures which require nonnegative actuator limits to maintain positive cable tensions. The developed algorithms are demonstrated in case studies applied to a cable-driven parallel manipulator with 2-degrees-of-freedom and three cables and to a 3-RRR parallel manipulator. The approaches used in this paper provide guaranteed results and are based on methods utilizing interval analysis techniques for the representation of end-effector poses and design parameters.

Workspace Representation of Parallel Manipulators Using the Finite Twist Method

1996 ◽  
Author(s):  
H. Singh ◽  
J. S. Dai ◽  
D. R. Kerr
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Image Space ◽  
End Effector ◽  
Unique Position ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Position And Orientation ◽  
The Individual ◽  
Established Technique

Abstract A method has been developed that successfully represents the workspace of a parallel manipulator within a finite twist image space. A point in this space represents a unique position and orientation of the end effector. The method of analysis is based upon the established technique of simplifying the parallel manipulator, by modelling each leg as an independent serial manipulator. The workspace corresponding to each serial manipulator is mapped onto the image space to produce a hyper-volume. The intersection of the individual hyper-volumes represents the workspace of the complete parallel manipulator. Since the hyper-volume corresponds to all possible positions attainable by the end effector, this represents the reachable workspace. Within the reachable workspace there lies subsets of volumes in ⮲3 that correspond to all possible orientations attainable. Such volumes represent the dextrous workspace. Although the method is illustrated by the use of a Stewart platform, it is equally applicable to the general parallel manipulator. The method is demonstrated successfully by the use of a 3 legged, 3-DOF planar parallel manipulator.

Closed-Form Determination of the Location of a Rigid Body by Seven In-Parallel Linear Transducers

1996 ◽  
Author(s):  
Carlo Innocenti
Keyword(s):  
Rigid Body ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Body Location ◽  
Position And Orientation ◽  
General Geometry ◽  
Two Bodies

Abstract The paper presents an original analytic procedure for unambiguously determining the relative position and orientation (location) of two rigid bodies based on the readings from seven linear transducers. Each transducer connects two points arbitrarily chosen on the two bodies. The sought-for rigid-body location simply results by solving linear equations. The proposed procedure is suitable for implementation in control of fully-parallel manipulators with general geometry. A numerical example shows application of the reported results to a case study.

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.

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