Inverse Kinematics for Planar Parallel Manipulators

1997 ◽  
Author(s):  
Robert L. Williams ◽  
Brett H. Shelley
Keyword(s):  
Inverse Kinematics ◽  
Broad Class ◽  
Parallel Manipulators ◽  
End Effector ◽  
Serial Chain ◽  
Prismatic Joints ◽  
Inverse Solutions ◽  
Three Degree Of Freedom ◽  
Serial Chains ◽  
Planar Parallel Manipulators

Abstract This paper presents algebraic inverse position and velocity kinematics solutions for a broad class of three degree-of-freedom planar in-parallel-actuated manipulators. Given an end-effector pose and rate, all active and passive joint values and rates are calculated independently for each serial chain connecting the ground link to the end-effector link. The solutions are independent of joint actuation. Seven serial chains consisting of revolute and prismatic joints are identified and their inverse solutions presented. To reduce computations, inverse Jacobian matrices for overall manipulators are derived to give only actuated joint rates. This matrix yields conditions for invalid actuation schemes. Simulation examples are given.

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.

The Synthesis of Planar Parallel Manipulators with a Genetic Algorithm

1999 ◽  
Vol 121 (4) ◽  
pp. 533-537 ◽  
Author(s):  
R. Boudreau ◽  
C. M. Gosselin
Keyword(s):  
Genetic Algorithm ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Degree Of Freedom ◽  
Natural Evolution ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Genetic Algorithm Approach ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

This paper presents a genetic algorithm approach for the synthesis of planar three-degree-of-freedom parallel manipulators. A genetic algorithm is an optimization method inspired by natural evolution. As in nature, the fittest members of a population are given better chances of reproducing and transmitting part of their genetic heritage to the next generation. This leads to stronger and stronger generations which evolve towards the solution of the problem. For the applications studied here, the individuals in the population consist of the architectural parameters of the manipulators. The algorithm optimizes these parameters to obtain a workspace as close as possible to a prescribed working area. For each individual of the population, the geometric description of the workspace can be obtained. The algorithm then determines the intersection between the prescribed workspace and the actual workspace, and minimizes the area of the regions that do not intersect. The method is applied to two planar three-degree-of-freedom parallel manipulators, one with prismatic joints and one with revolute joints.

The Synthesis of Planar Parallel Manipulators With a Genetic Algorithm

1998 ◽  
Author(s):  
Roger Boudreau ◽  
Clément M. Gosselin
Keyword(s):  
Genetic Algorithm ◽  
Parallel Manipulators ◽  
Optimization Method ◽  
Degree Of Freedom ◽  
Natural Evolution ◽  
Revolute Joints ◽  
Prismatic Joints ◽  
Genetic Algorithm Approach ◽  
Three Degree Of Freedom ◽  
Planar Parallel Manipulators

Abstract This paper presents a genetic algorithm approach for the synthesis of planar three-degree-of-freedom parallel manipulators. A genetic algorithm is an optimization method inspired by natural evolution. As in nature, the fittest members of a population are given better chances of reproducing and transmitting part of their genetic heritage to the next generation. This leads to stronger and stronger generations which evolve towards the solution of the problem. For the applications studied here, the individuals in the population consist of the thirteen architectural parameters of the manipulators. The algorithm optimizes these parameters to obtain a workspace as close as possible to a prescribed working area. For each individual of the population, the geometric description of the workspace can be obtained. The algorithm then determines the intersection between the prescribed workspace and the actual workspace, and minimizes the area of the regions that do not intersect. The method is applied to two planar three-degree-of-freedom parallel manipulators, one with prismatic joints and one with revolute joints.

Parametric Design of a Spherical Eight-Bar Linkage Based on a Spherical Parallel Manipulator

2008 ◽  
Vol 1 (1) ◽  
Author(s):  
Gim Song Soh ◽  
J. Michael McCarthy
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Parametric Design ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
End Effector ◽  
Arbitrary Base ◽  
Three Degree Of Freedom ◽  
Spherical Parallel Manipulator

This paper presents a procedure that determines the dimensions of two constraining links to be added to a three degree-of-freedom spherical parallel manipulator so that it becomes a one degree-of-freedom spherical (8, 10) eight-bar linkage that guides its end-effector through five task poses. The dimensions of the spherical parallel manipulator are unconstrained, which provides the freedom to specify arbitrary base attachment points as well as the opportunity to shape the overall movement of the linkage. Inverse kinematics analysis of the spherical parallel manipulator provides a set of relative poses between all of the links, which are used to formulate the synthesis equations for spherical RR chains connecting any two of these links. The analysis of the resulting spherical eight-bar linkage verifies the movement of the system.

Characterization of Workspaces of Parallel Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 368-375 ◽  
Author(s):  
V. Kumar
Keyword(s):  
Parallel Manipulators ◽  
Geometric Optimization ◽  
Reachable Workspace ◽  
Serial Chain ◽  
Kinematic Performance ◽  
Serial Chains ◽  
Manipulator Control ◽  
General Method

The workspaces and kinematic characterization of serial chain manipulator geometries and the geometric optimization have been studied extensively. Much less is known about workspaces for manipulation systems which possess several serial chains arranged in parallel. In this paper, two well known workspaces, the reachable workspace and the dexterous workspace, are investigated for parallel manipulators. A general method for obtaining these workspaces is presented. The existence of numerous special configurations in the workspace present problems in manipulator control. Therefore the controllably dexterous workspace is proposed as a useful measure of kinematic performance. The methodology of delineating the workspaces and its limitations are illustrated with examples.

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.

Simulation on Trajectory Planning of 6R Manipulator Based on the Shortest Distance Criterion

2014 ◽  
Vol 602-605 ◽  
pp. 942-945
Author(s):  
Qing Qing Huang ◽  
Guang Feng Chen ◽  
Jiang Hua Li ◽  
Xin Wei
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Spline Interpolation ◽  
Algebraic Method ◽  
End Effector ◽  
Cartesian Space ◽  
Shortest Distance ◽  
Inverse Solutions ◽  
Group Inverses ◽  
Forward And Inverse Kinematics

This paper concerns the trajectory planning and simulation for 6R Manipulator. First, algebraic method was used to deduce the forward and inverse kinematics of 6R manipulator. All inverse solutions were expressed in atan2 to eliminate redundant roots to get the corresponding inverse formula. For the trajectory planning of manipulator in Cartesian space, using the cubic spline interpolation to get the drive function of joint, getting a unique solution from eight group inverses by the shortest distance criterion, and then obtained the actual end-effector trajectory. Using Matlab to verify the proposed trajectory planning method, validated results show that the proposed algorithm is feasible and effective.

An inverse position analysis of five-bar planar parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (2) ◽  
pp. 195-201 ◽  
Author(s):  
Gürsel Alici
Keyword(s):  
Parallel Manipulators ◽  
Joint Space ◽  
Computationally Efficient ◽  
Simple Method ◽  
Cartesian Coordinates ◽  
Reachable Workspace ◽  
Prismatic Joints ◽  
Inverse Position Analysis ◽  
Translational Joint ◽  
Planar Parallel Manipulators

In this paper, we present a simple method to obtain joint inputs needed to attain any point in the reachable workspace of a class of five-bar planar parallel manipulators which are based on five rigid links and five single degree of freedom joints – revolute and prismatic joints. Depending on the topology of the manipulators, two mathematical expressions describing the path traced by the tip of two links connected to each other are obtained and solved simultaneously in order to determine the intersection points of the two paths which are the Cartesian coordinates of the connection points for the links. For the class of manipulators considered in this study, one of the links is the link activated by an actuator fixed to the ground. So, rotational and/or translational joint inputs can be determined from the Cartesian coordinates of the tip of the activated links. Sylvester's dialytic elimination method is employed to solve the equations. Such a methodology is easy to implement, computationally efficient and sound to compute all possible solutions. A numerical example is provided for each manipulator and the inverse position solutions are verified by substituting them into forward position equations. It is concluded that the proposed method is useful in trajectory planning and control of five-bar planar parallel manipulators in joint space.

scholarly journals A Design System for Eight-Bar Linkages as Constrained 4R Serial Chains

2015 ◽  
Vol 8 (1) ◽  
Author(s):  
Kaustubh H. Sonawale ◽  
J. Michael McCarthy
Keyword(s):  
Random Search ◽  
Design System ◽  
End Effector ◽  
Serial Chain ◽  
Straight Line ◽  
Tolerance Zones ◽  
Serial Chains

This paper presents a design system for planar eight-bar linkages that adds three RR constraints to a user-specified 4R serial chain. R denotes a revolute, or hinged, joint. There are 100 ways in which these constraints can be added to yield as many as 3951 different linkages. An analysis routine based on the Dixon determinant evaluates the performance of each linkage candidate and determines the feasible designs that reach the task positions in a single assembly. A random search within the user-specified tolerance zones around the task specifications is iterated in order to increase the number of linkage candidates and feasible designs. The methodology is demonstrated with the design of rectilinear eight-bar linkages that guide an end-effector through five parallel positions along a straight line.

scholarly journals Kinematic Synthesis of Spatial Serial Chains Using Clifford Algebra Exponentials

2006 ◽  
Vol 220 (7) ◽  
pp. 953-968 ◽  
Author(s):  
A Perez-Gracia ◽  
J M McCarthy
Keyword(s):  
Clifford Algebra ◽  
Robotic System ◽  
Exponential Form ◽  
Kinematic Synthesis ◽  
End Effector ◽  
Dual Quaternions ◽  
Serial Chain ◽  
Joint Parameters ◽  
Position And Orientation ◽  
Serial Chains

This article presents a formulation of the design equations for a spatial serial chain that uses the Clifford algebra exponential form of its kinematics equations. This is the even Clifford algebra C+( P3), known as dual quaternions. These equations define the position and orientation of the end effector in terms of rotations or translations about or along the joint axes of the chain. Because the coordinates of these axes appear explicitly, specifying a set of task positions these equations can be solved to determine the location of the joints. At the same time, joint parameters or certain dimensions are specified to ensure that the resulting robotic system has specific features.

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