Differential kinematics of parallel manipulators using Assur virtual chains

2009 ◽  
Vol 223 (7) ◽  
pp. 1697-1711 ◽  
Author(s):  
A Campos ◽  
R Guenther ◽  
D Martins
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Kinematic Constraints ◽  
Passive Joint ◽  
Planar Parallel Manipulator ◽  
Stewart Gough Platform ◽  
Homogeneous Linear

This article introduces the concept of Assur virtual chains and its applications in differential kinematics of parallel manipulators. Using Assur virtual chains, the differential kinematics has a simple matricial formulation and the choice between direct and inverse kinematics is reduced to select primary variables in a homogeneous linear system. Assur virtual chains are also useful for obtaining information about the relative movements or to imposing particular kinematic constraints between two links of a kinematic chain. Additionally, a new systematic algorithm is established to analytically eliminate passive joint velocities and calculate the Jacobian matrices. This elimination approach is based on screw theory concepts such as twist, wrench, and reciprocity; also, graph theory is used for kinematic chain representation. At the end of the article, the method is applied to a 3RRR planar parallel manipulator and a general universal-prismatic-spheric Stewart—Gough platform.

Type Synthesis of 3-DOF Spherical Parallel Manipulators Based on Screw Theory1

2004 ◽  
Vol 126 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Xianwen Kong ◽  
Cle´ment M. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
General Procedure ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Type Synthesis ◽  
Validity Condition ◽  
First Time ◽  
Spherical Parallel Manipulator ◽  
Selection Of

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time.

scholarly journals A Five-Bar Planar Parallel Manipulator with Two End-Effectors

2018 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Ramon Rodriguez-Castro ◽  
Luciano Perez-Gonzalez ◽  
Carlos R. Aguilar-Najera ◽  
Alvaro Sanchez-Rodriguez
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Intermediate Step ◽  
Euclidean Group ◽  
Planar Parallel Manipulator ◽  
Special Software ◽  
End Effectors ◽  
Klein Form

Parallel manipulators with multiple end-effectors bring us interesting advantages over conventional parallel manipulators such as improved manipulability, workspace and avoidance of singularities. In this work the kinematics of a five-bar planar parallel manipulator equipped with two end-effectors is approached by means of the theory of screws. As an intermediate step the displacement analysis of the robot is also investigated. The input-output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. In that regard the Klein form of the Lie algebra se(3) of the Euclidean group SE(3) plays a central role. In order to exemplify the method of kinematic analysis, a case study is included. Furthermore, the numerical results obtained by means of the theory of screws are confirmed with the aid of special software like ADAMS.TM

scholarly journals Pa<sup>2</sup> kinematic bond in translational parallel manipulators

2018 ◽  
Vol 9 (1) ◽  
pp. 25-39 ◽  
Author(s):  
Alfonso Hernández ◽  
Erik Macho ◽  
Mónica Urízar ◽  
Víctor Petuya ◽  
Zhen Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
The Other ◽  
Practical Application ◽  
Promising Alternative ◽  
Revolute Joints ◽  
Prismatic Joints

Abstract. The Pa2 pair is composed of two intertwined articulated parallelograms connecting in parallel two links of a kinematic chain. This pair has two translational degrees of freedom leading to a translational plane variable with the position. Currently, the Pa2 pair appears in conceptual designs presented in recent papers. However, its practical application is very limited. One of the reasons for this can be the high number of redundant constraints it has. But, it has to be considered that most of them can be eliminated by replacing wisely the revolute joints by spherical joints. On the other side, the structure of the Pa2 pair contributes to increase the global stiffness of the kinematic chain in which it is mounted. Also, its implementation is a promising alternative to the problematic passive prismatic joints. In this paper, the Pa2 pairs are used in the design of a 3 − P Pa2 parallel manipulator. The potentiality of this design is evaluated and proven after doing the following analyses: direct and inverse kinematics, singularity study, and workspace computation and assessment.

scholarly journals Acceleration Analysis of 3-DOF Planar Parallel Manipulators by Means of Screw Theory

2016 ◽  
Vol 45 (2) ◽  
pp. 89-95
Author(s):  
Soheil Zarkandi
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Second Order ◽  
Degree Of Freedom ◽  
Planar Parallel Manipulator ◽  
Acceleration Analysis ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper deals with the second order kinematics of three degree-of-freedom (DOF) planar parallel manipulators. The simple and compact expressions are derived for both the inverse and forward acceleration analyses using screw theory. Moreover, as an example, a 3-DOF planar parallel manipulator is introduced and its kinematics is analyzed using the proposed method.

Kinematics analysis of a redundantly actuated 4-RUU translational parallel manipulator and its nonredundant 3-RUU counterpart

2016 ◽  
Vol 231 (17) ◽  
pp. 3238-3249 ◽  
Author(s):  
Haibo Qu ◽  
Sheng Guo ◽  
Ying Zhang
Keyword(s):  
Comparative Study ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Kinematics Analysis ◽  
Universal Joint ◽  
Torque Distribution ◽  
Redundantly Actuated

This paper presents a comparative study of the kinematics and torque distribution performance of a nonredundant 3-RUU and a redundantly actuated 4-RUU (R: revolute joint, U: universal joint) translational parallel manipulators. First, the reason for unexpected rotations is analyzed based on screw theory and a redundantly actuated 4-RUU translational parallel manipulator is presented to eliminate the unexpected rotations. Then, the degrees of freedom, inverse kinematics, Jacobian matrices, and workspace of 3-RUU and 4-RUU parallel manipulators are analyzed. Finally, a comparative study of torque distribution is performed. The results show that the redundantly actuated 4-RUU parallel manipulator can overcome the unexpected rotations and possesses an improved torque distribution, compared with the nonredundant 3-RUU parallel manipulator.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

scholarly journals Workspace Delineation of Cable-Actuated Parallel Manipulators

2004 ◽  
Author(s):  
Ethan Stump ◽  
Vijay Kumar
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Extensive Literature ◽  
Reachable Workspace ◽  
Planar Parallel Manipulator ◽  
Analytic Expressions

While there is extensive literature available on parallel manipulators in general, there has been much less attention given to cable-driven parallel manipulators. In this paper, we address the problem of analyzing the reachable workspace using the tools of semi-definite programming. We build on earlier work [1, 2] done using similar techniques by deriving limiting conditions that allow us to compute analytic expressions for the boundary of the reachable workspace. We illustrate this computation for a planar parallel manipulator with four actuators.

Singularity robust inverse dynamics of planar 2-RPR parallel manipulators

2004 ◽  
Vol 218 (7) ◽  
pp. 721-730 ◽  
Author(s):  
S Kemal Ider
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Full Rank ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
Dynamic Equations ◽  
Revolute Joints ◽  
Planar Parallel Manipulator ◽  
Pass Through ◽  
Full Utilization

In planar parallel robots, limitations occur in the functional workspace because of interference of the legs with each other and because of drive singularities where the actuators lose control of the moving platform and the actuator forces grow without bounds. A 2-RPR (revolute, prismatic, revolute joints) planar parallel manipulator with two legs that minimizes the interference of the mechanical components is considered. Avoidance of the drive singularities is in general not desirable since it reduces the functional workspace. An inverse dynamics algorithm with singularity robustness is formulated allowing full utilization of the workspace. It is shown that if the trajectory is planned to satisfy certain conditions related to the consistency of the dynamic equations, the manipulator can pass through the drive singularities while the actuator forces remain stable. Furthermore, for finding the actuator forces in the vicinity of the singular positions a full rank modification of the dynamic equations is developed. A deployment motion is analysed to illustrate the proposed approach.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

2005 ◽  
Vol 127 (4) ◽  
pp. 550-563 ◽  
Author(s):  
C. K. Kevin Jui ◽  
Qiao Sun
Keyword(s):  
Motion Planning ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Parallel Manipulators ◽  
Path Tracking ◽  
Singularity Avoidance ◽  
Design Complexity ◽  
Actuation Redundancy ◽  
Planar Parallel Manipulator ◽  
Simulation Results

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

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