A planar quaternion approach to the kinematic synthesis of a parallel manipulator

Robotica ◽  
1997 ◽  
Vol 15 (4) ◽  
pp. 361-365 ◽  
Author(s):  
Andrew P. Murray ◽  
François Pierrot ◽  
Pierre Dauchez ◽  
J. Michael McCarthy
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Constraint Manifold ◽  
Planar Parallel Manipulators

In this paper we present a technique for designing planar parallel manipulators with platforms capable of reaching any number of desired poses. The manipulator consists of a platform connected to ground by RPR chains. The set of positions and orientations available to the end-effector of a general RPR chain is mapped into the space of planar quaternions to obtain a quadratic manifold. The coefficients of this constraint manifold are functions of the locations of the base and platform R joints and the distance between them. Evaluating the constraint manifold at each desired pose and defining the limits on the extension of the P joint yields a set of equations. Solutions of these equations determine chains that contain the desired poses as part of their workspaces. Parallel manipulators that can reach the prescribed workspace are assembled from these chains. An example shows the determination of three RPR chains that form a manipulator able to reach a prescribed workspace.

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.

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.

Kinematic analysis and workspace determination of hexarot-a novel 6-DOF parallel manipulator with a rotation-symmetric arm system

Robotica ◽  
2014 ◽  
Vol 33 (08) ◽  
pp. 1686-1703 ◽  
Author(s):  
Mohammad Reza Chalak Qazani ◽  
Siamak Pedrammehr ◽  
Arash Rahmani ◽  
Behzad Danaei ◽  
Mir Mohammad Ettefagh ◽  
...  
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
End Effector ◽  
High Acceleration ◽  
Workspace Analysis ◽  
Rotation Symmetric ◽  
Cloud Of Points

SUMMARYParallel mechanisms possess several advantages such as the possibilities for high acceleration and high accuracy positioning of the end effector. However, most of the proposed parallel manipulators suffer from a limited workspace. In this paper, a novel 6-DOF parallel manipulator with coaxial actuated arms is introduced. Since parallel mechanisms have more workspace limitations compared to that of serial mechanisms, determination of the workspace in parallel manipulators is of the utmost importance. For finding position, angular velocity, and acceleration, in this paper, inverse and forward kinematics of the mechanism are studied and after presenting the workspace limitations, workspace analysis of the hexarot manipulator is performed by using MATLAB software. Next, using the obtained cloud of points from simulation, the overall borders of the workspace are illustrated. Finally, it is shown that this manipulator has the important benefits of combining a large positional workspace in relation to its footprint with a sizable range of platform rotations.

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.

Wrench capabilities of planar parallel manipulators. Part I: Wrench polytopes and performance indices

Robotica ◽  
2008 ◽  
Vol 26 (6) ◽  
pp. 791-802 ◽  
Author(s):  
Flavio Firmani ◽  
Alp Zibil ◽  
Scott B. Nokleby ◽  
Ron P. Podhorodeski
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Linear Mapping ◽  
Redundant Manipulators ◽  
Task Space ◽  
Performance Indices ◽  
Study Case ◽  
And Performance ◽  
Planar Parallel Manipulators

SUMMARYThis paper is organized in two parts. In Part I, the wrench polytope concept is presented and wrench performance indices are introduced for planar parallel manipulators (PPMs). In Part II, the concept of wrench capabilities is extended to redundant manipulators and the wrench workspace of different PPMs is analyzed. The end-effector of a PPM is subject to the interaction of forces and moments. Wrench capabilities represent the maximum forces and moments that can be applied or sustained by the manipulator. The wrench capabilities of PPMs are determined by a linear mapping of the actuator output capabilities from the joint space to the task space. The analysis is based upon properly adjusting the actuator outputs to their extreme capabilities. The linear mapping results in a wrench polytope. It is shown that for non-redundant PPMs, one actuator output capability constrains the maximum wrench that can be applied (or sustained) with a plane in the wrench space yielding a facet of the polytope. Herein, the determination of wrench performance indices is presented without the expensive task of generating polytopes. Six study cases are presented and performance indices are derived for each study case.

Determination of the Workspace of 6-DOF Parallel Manipulators

1989 ◽  
Author(s):  
C. Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Geometrical Properties ◽  
Cartesian Space ◽  
Six Degree Of Freedom

Abstract This paper presents an algorithm for the determination of the workspace of parallel manipulators. The method described here, which is based on geometrical properties of the workspace, leads to a simple graphical representation of the regions of the three-dimensional Cartesian space that are attainable by the manipulator with a given orientation of the platform. Moreover, the volume of the workspace can be easily computed by performing an integration on its boundary, which is obtained from the algorithm. Examples are included to illustrate the application of the method to a six-degree-of-freedom fully-parallel manipulator.

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.

Determination of the Singularity Loci of Spherical Three-Degree-of-Freedom Parallel Manipularors

1992 ◽  
Author(s):  
Clément M. Gosselin ◽  
Jaouad Sefrioui
Keyword(s):  
Graphical Representation ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
End Effector ◽  
Cartesian Space ◽  
Singularity Locus ◽  
Three Degree Of Freedom ◽  
Analytical Expressions

Abstract In this paper, an algorithm for the determination of the singularity loci of spherical three-degree-of-freedom parallel manipulators with prismatic atuators is presented. These singularity loci, which are obtained as curves or surfaces in the Cartesian space, are of great interest in the context of kinematic design. Indeed, it has been shown elsewhere that parallel manipulators lead to a special type of singularity which is located inside the Cartesian workspace and for which the end-effector becomes uncontrollable. It is therfore important to be able to identify the configurations associated with theses singularities. The algorithm presented is based on analytical expressions of the determinant of a Jacobian matrix, a quantity that is known to vanish in the singular configurations. A general spherical three-degree-of-freedom parallel manipulator with prismatic actuators is first studied. Then, several particular designs are investigated. For each case, an analytical expression of the singularity locus is derived. A graphical representation in the Cartesian space is then obtained.

FORCE-UNCONSTRAINED POSES FOR PARALLEL MANIPULATORS WITH REDUNDANT ACTUATED BRANCHES

2005 ◽  
Vol 29 (3) ◽  
pp. 343-356 ◽  
Author(s):  
Flavio Firmani ◽  
Ron P. Podhorodeski
Keyword(s):  
Dimensional Space ◽  
Parallel Manipulators ◽  
End Effector ◽  
Input And Output ◽  
Planar Manipulators ◽  
Order Polynomial ◽  
Prismatic Joints ◽  
Redundantly Actuated ◽  
Actuated Joints ◽  
Planar Parallel Manipulators

A study of the effect of including a redundant actuated branch on the existence of force-unconstrained configurations for a planar parallel layout of joints is presented1. Two methodologies for finding the force-unconstrained poses are described and discussed. The first method involves the differentiation of the nonlinear kinematic constraints of the input and output variables with respect to time. The second method makes use of the reciprocal screws associated with the actuated joints. The force-unconstrained poses of non-redundantly actuated planar parallel manipulators can be mathematically expressed by means of a polynomial in terms of the three variables that define the dimensional space of the planar manipulator, i.e., the location and orientation of the end-effector. The inclusion of redundant actuated branches leads to a system of polynomials, i.e., one additional polynomial for each redundant branch added. Elimination methods are employed to reduce the number of variables by one for every additional polynomial. This leads to a higher order polynomial with fewer variables. The roots of the resulting polynomial describe the force-unconstrained poses of the manipulator. For planar manipulators it is shown that one order of infinity of force-unconstrained configurations is eliminated for every actuated branch, beyond three, added. As an example, the four-branch revolute-prismatic-revolute mechanism (4-RPR), where the prismatic joints are actuated, is presented.

Sign in / Sign up

Export Citation Format

Share Document