Determination of the closed-form workspace area expression and dimensional optimization of planar parallel manipulators

Robotica ◽  
2016 ◽  
Vol 35 (10) ◽  
pp. 2056-2075 ◽  
Author(s):  
M. Ganesh ◽  
Banke Bihari ◽  
Vijay Singh Rathore ◽  
Dhiraj Kumar ◽  
Chandan Kumar ◽  
...  
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Solution Space ◽  
Optimization Procedure ◽  
Parallel Manipulators ◽  
Force Transmission ◽  
Workspace Analysis ◽  
Planar Parallel Manipulator ◽  
Transmission Index ◽  
Planar Parallel Manipulators

SUMMARYOptimization is an important step in the design and development of a planar parallel manipulator. For optimization processes, workspace analysis is a crucial and preliminary objective. Generally, the workspace analysis for such manipulators is carried out using a non-dimensional approach. For planar parallel manipulators of two degrees of freedom (2-DOF), a non-dimensional workspace analysis is very advantageous. However, it becomes very difficult in the case of 3-DOF and higher DOF manipulators because of the complex shape of the workspace. In this study, the workspace shape is classified as a function of the geometric parameters, and the closed-form area expressions are derived for a constant orientation workspace of a three revolute–revolute–revolute (3-RRR) planar manipulator. The approach is also shown to be feasible for different orientations of a mobile platform. An optimization procedure for the design of planar 3-RRR manipulators is proposed for a prescribed workspace area. It is observed that the closed-form area expression for all the possible shapes of the workspace provides a larger solution space, which is further optimized considering singularity, mass of the manipulator, and a force transmission index.

Workspace Analysis and Going through Singularities of 5-Bar Symmetric Planar Parallel Manipulator by Automated Selective Actuation Mechanism

2012 ◽  
Vol 588-589 ◽  
pp. 1664-1668
Author(s):  
Syam Sundar ◽  
Vijay S. Rathore ◽  
Manoj K. Sahi ◽  
V. Upendran ◽  
Anjan Kumar Dash
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
New Approach ◽  
Serial Manipulators ◽  
Actuation Mechanism ◽  
Geometric Conditions ◽  
Workspace Analysis ◽  
Planar Parallel Manipulator ◽  
Planar Parallel Manipulators

In this article‚ a new approach is presented to determine the various shapes of workspaces of 5 bar symmetric planar parallel manipulators. Here the shape of the workspace is determined by the number of ways the workspaces of the two serial manipulators intersect with each other. Geometric conditions are established in each case and area of each shape of workspace is determined in closed form. Singularity is another important consideration in the design of parallel manipulators. In this paper, an approach is presented to go through the singularity points using an automatic selective actuation mechanism. A prototype 5-bar planar manipulator is fabricated along with an automatic selective actuation mechanism demonstrating the manipulator going through the singularity points.

Mobility, Kinematic Analysis, and Dimensional Optimization of New Three-Degrees-of-Freedom Parallel Manipulator With Actuation Redundancy

2017 ◽  
Vol 9 (4) ◽  
Author(s):  
Lingmin Xu ◽  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Qiaohong Chen
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Force Transmission ◽  
Transmission Index ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Force Transmissibility ◽  
Solution Velocity ◽  
Three Degrees Of Freedom

Parallel manipulators (PMs) with redundant actuation are attracting increasing research interest because they have demonstrated improved stiffness and fewer singularities. This paper proposes a new redundantly actuated parallel manipulator that has three degrees-of-freedom (DOFs) and four limbs. The proposed manipulator is a 2UPR-2PRU parallel manipulator (where P represents an actuated prismatic joint, R represents a revolute joint, and U represents a universal joint) that is actuated using four prismatic joints; two of these joints are mounted on the base to reduce the movable mass. Mobility analysis shows that the moving platform has two rotational DOFs and one translational DOF. First, the inverse displacement solution, velocity, and singularity analyses are discussed. Next, the local transmission index (LTI) and the good transmission workspace are used to evaluate the motion/force transmissibility of the 2UPR-2PRU parallel manipulator. Finally, the parameter-finiteness normalization method (PFNM) is used to produce an optimal design that considers the good transmission workspace. It is thus shown that the motion/force transmission of the proposed manipulator is improved by optimizing the link parameters.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

New Indices for Optimal Design of Redundantly Actuated Parallel Manipulators

2016 ◽  
Vol 9 (1) ◽  
Author(s):  
Qinchuan Li ◽  
Ningbin Zhang ◽  
Feibo Wang
Keyword(s):  
Optimal Design ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Mean Value ◽  
Transmission Performance ◽  
Transmission Index ◽  
Redundantly Actuated ◽  
Lower Mobility ◽  
Six Dof ◽  
Force Transmissibility

Redundantly actuated parallel manipulators (PMs) receive growing interest due to their reduced singularity and enlarged workspace. This paper proposes new indices for optimal design and analysis of redundantly actuated PMs by evaluating their motion/force transmissibility. First, we proposed a method to extract a multi-DOF (degrees-of-freedom) redundantly actuated PM into several subsidiary one-DOF PMs with two or more actuators by locking some actuators in an ergodic manner. Then, a new index of output transmission performance is proposed by investigating the mean value of the instantaneous power produced by the multiple actuation wrenches and one twist of the moving platform of one-DOF PMs. A local transmission index (LTI) is defined as the minimum value of the index of output and input transmission performance. A global transmission index (GTI) is then established based on the LTI. The proposed LTI and GTI are coordinate-free and have clear physical interpretation. Finally, the validity and universality of the new indices are demonstrated by optimization and analysis of redundantly actuated lower-mobility PMs with extra articulated six-DOF or limited-DOF limbs.

Geometry and Position Analysis of a Novel Class of Hybrid Manipulators

1994 ◽  
Author(s):  
Change-de Zhang ◽  
Shin-Min Song
Keyword(s):  
Closed Form ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Parallel Mechanisms ◽  
Serial Manipulators ◽  
Closed Form Solutions ◽  
Position Analysis ◽  
Hybrid Manipulator ◽  
Load Carrying ◽  
Inverse Position Analysis

Abstract This paper presents a novel class of hybrid manipulators composed of two serially connected parallel mechanisms, each of which has three degrees of freedom. The lower and upper platforms respectively control the position and orientation of the end-effector. The advantages of this type of hybrid manipulator are larger workspace (as compared with parallel manipulators) and better rigidity and higher load-carrying capability (as compared with serial manipulators). The closed-form solutions of the forward and inverse position analyses are discussed. For forward position analysis, it is shown that the resultant equation for the positional mechanism is an 8-th order, a 6-th order, a 4-th order, or a 2-nd order polynomial, depending on the geometry and joint types of the passive subchain, while for the orientational mechanism, it is an 8-th order, or a 2-nd polynomial depending on the geometry. For inverse position analysis, it is demonstrated that the positional and orientational mechanisms both possess analytical closed-form solutions.

Kinematic analysis of overconstrained manipulators with partial subspaces using decomposition method

Robotica ◽  
2021 ◽  
pp. 1-16
Author(s):  
Özgün Selvi
Keyword(s):  
Kinematic Analysis ◽  
Decomposition Method ◽  
Degrees Of Freedom ◽  
Additional Data ◽  
Parallel Manipulators ◽  
Inverse Kinematic ◽  
Velocity Analysis ◽  
Workspace Analysis ◽  
Inverse Kinematic Analysis ◽  
Inverse Velocity

SUMMARY Overconstrained manipulators in lower subspaces with unique motions can be created and analyzed. However, far too little attention has been paid to creating a generic method for overconstrained manipulators kinematic analysis. This study aimed to evaluate a generic methodology for kinematic analysis of overconstrained parallel manipulators with partial subspaces (OPM-PS) using decomposition to parallel manipulators (PMs) in lower subspaces. The theoretical dimensions of the method are depicted, and the use of partial subspace for overconstrained manipulators is portrayed. The methodology for the decomposition method is described and exemplified by designing and evaluating the method to two overconstrained manipulators with 5 degrees of freedom (DoF) and 3 DoF. The inverse kinematic analysis is detailed with position analysis and Jacobian along with the inverse velocity analysis. The workspace analysis for the manipulators using the methodology is elaborated with numerical results. The results of the study show that OPM-PS can be decomposed into PMs with lower subspace numbers. As imaginary joints are being utilized in the proposed methodology, it will create additional data to consider in the design process of the manipulators. Thus, it becomes more beneficial in design scenarios that include workspace as an objective.

Continuous Workspace Analysis, Synthesis and Optimization of Wire Robots

2008 ◽  
Author(s):  
Tobias Bruckmann ◽  
Lars Mikelsons ◽  
Manfred Hiller ◽  
Dieter Schramm
Keyword(s):  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Force Distribution ◽  
End Effector ◽  
Analysis Methods ◽  
Workspace Analysis ◽  
Pulling Forces ◽  
Discrete Methods ◽  
Computationally Expensive ◽  
Calculation Grid

Wire robots (also called Tendon-based parallel manipulators) use a movable end-effector which is connected to a machine frame by motor driven tendons. Since tendons can transmit only pulling forces, at least m = n + 1 cables are needed to tense a system having n degrees-of-freedom. The resulting redundancy gives m − n degrees-of-freedom in the wire force distribution, making workspace analysis a complex and computationally expensive task. Discrete methods are widely used to solve this problem, but their drawback is that intermediate points on the discrete calculation grid are neglected which may lead to false results. This paper provides detailed algorithms for continuous workspace analysis for wire robots which avoid the discretization and have additional advantages. Especially, it is easy to extend the analysis methods to methods usable for the workspace synthesis.

Comparative Kinematic Analysis and Design Optimization of Redundant and Nonredundant Planar Parallel Manipulators Intended for Haptic Use

Robotica ◽  
2019 ◽  
Vol 38 (8) ◽  
pp. 1463-1477 ◽  
Author(s):  
Houssem Saafi ◽  
Houssein Lamine
Keyword(s):  
Design Optimization ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Kinematic Model ◽  
Parallel Manipulators ◽  
Geometric Parameters ◽  
Analysis And Design ◽  
Planar Parallel Manipulator ◽  
Forward Kinematic ◽  
Planar Parallel Manipulators

SUMMARYThis paper investigates a comparative kinematic analysis between nonredundant and redundant 2-Degree Of Freedom parallel manipulators. The nonredundant manipulator is based on the Five-Bar mechanism, and the redundant one is a 3-RRR planar parallel manipulator. This study is aimed to select the best structure for a haptic application. This latter requires a mechanism with a desired workspace of 10 cm × 10 cm and an admissible force of 5 N in all directions. The analysis criteria are the accuracy of the forward kinematic model and the required actuator torques. Thereby, the geometric parameters of the two structures are optimized in order to satisfy the required workspace such that parallel singularities are overcome. The analysis showed that the nonredundant optimally designed manipulator is more suitable for the haptic application.

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.

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