Formulation of Unique Form of Screw Based Jacobian for Lower Mobility Parallel Manipulators

2010 ◽  
Vol 3 (1) ◽  
Author(s):  
Man Bok Hong ◽  
Yong Je Choi
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Unique Form ◽  
Kinematic Chains ◽  
Revolute Joints ◽  
Serial Chain ◽  
Velocity Relation ◽  
Lower Mobility ◽  
Serial Chains ◽  
Inverse Velocity

In this paper, the unique form of the screw based Jacobian is suggested for lower mobility parallel manipulators. Utilizing the concept of the reciprocal Jacobian, the forward statics relation for each of the serial kinematic chains of a parallel manipulator can be first obtained and then used to derive both the forward statics and the inverse velocity relations of the manipulator. The screw based Jacobian of a parallel manipulator can be formulated from the inverse velocity relation in such a way that it consists of the reciprocal Jacobians of the serial kinematic chains. Since any reciprocal Jacobian is unique to the corresponding serial chain, the suggested form of the screw based Jacobian is also determined uniquely to the lower mobility parallel manipulator. Two examples are given to illustrate the proposed method, one for the 3DOF parallel manipulator with three identical prismatic-revolute-spherical joints-serial chains and the other for the 4DOF parallel manipulator with nonidentical serial chains (two spherical-prismatic-spherical- and one revolute-revolute-prismatic-revolute joints-serial chains).

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulator

2010 ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Parallel Manipulator ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
Kinematic Chains ◽  
Lie Bracket ◽  
Lower Mobility ◽  
Acceleration Analysis ◽  
Definition Of

This paper presents an approach for velocity and acceleration analyses of lower mobility parallel manipulators. Based on the definition of the acceleration motor, the forward/inverse velocity and acceleration equations are formulated with the goal to integrate the relevant analyses under a unified framework based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limb) is developed in an explicit and compact form using Lie bracket. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational moving capabilities is taken as example to illustrate the generality and effectiveness of this approach.

Analysis of Two Spherical Parallel Manipulators With Hidden Revolute Joints

2017 ◽  
Vol 9 (3) ◽  
Author(s):  
Ju Li ◽  
J. Michael McCarthy
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Internal Constraints ◽  
Quadric Surfaces ◽  
Revolute Joints ◽  
Serial Chain ◽  
Point Of Intersection ◽  
Spherical Parallel Manipulator

In this paper, we examine two spherical parallel manipulators (SPMs) constructed with legs that include planar and spherical subchains that combine to impose constraints equivalent to hidden revolute joints. The first has supporting serial chain legs constructed from three revolute joints with parallel axes, denoted R∥R∥R, followed by two revolute joints that have intersecting axes, denoted RR̂. The leg has five degrees-of-freedom and is denoted R∥R∥R-RR̂. Three of these legs can be assembled so the spherical chains all share the same point of intersection to obtain a spherical parallel manipulator denoted as 3-R∥R∥R-RR̂. The second spherical parallel manipulator has legs constructed from three revolute joints that share one point of intersection, denoted RRR̂, and a second pair of revolute joints with axes that intersect in a different point. This five-degree-of-freedom leg is denoted RRR̂-RR̂. The spherical parallel manipulator constructed from these legs is 3-RRR̂-RR̂. We show that the internal constraints of these two types of legs combine to create hidden revolute joints that can be used to analyze the kinematics and singularities of these spherical parallel manipulators. A quaternion formulation provides equations for the quartic singularity varieties some of which decompose into pairs of quadric surfaces which we use to classify these spherical parallel manipulators.

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.

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.

Direct Position Analysis in Analytical Form of Parallel Manipulators Generating Structures With Topology SR-2PS

2004 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Solution Procedure ◽  
Generic Structure ◽  
Kinematic Chains ◽  
Position Analysis ◽  
In Series ◽  
The One ◽  
Wide Family

A wide family of parallel manipulators (PMs) is the one that groups all the PMs with three legs where the legs become kinematic chains constituted of a passive spherical pair (S) in series with either a passive prismatic pair (P) or a passive revolute pair (R) when the actuators are locked. The topologies of the structures generated by these manipulators, when the actuators are locked, are ten. One out of these topologies is the SR-2PS topology (one SR leg and two PS legs). This paper presents an algorithm that determines all the assembly modes of the structures with topology SR-2PS in analytical form. The presented algorithm can be applied without changes to solve, in analytical form, the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked. In particular, the closure equations of a generic structure with topology SR-2PS are written. The eliminant of this system of equations is determined and the solution procedure is presented. Finally, the proposed procedure is applied to a real case. This work demonstrates that the solutions of the direct position analysis of any parallel manipulator which generates a SR-2PS structure when the actuators are locked are at most eight.

A novel class of generalized parallel manipulators with high rotational capability

2020 ◽  
Vol 234 (23) ◽  
pp. 4599-4619
Author(s):  
Chunxu Tian ◽  
Dan Zhang ◽  
Jian Liu
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Structural Characteristics ◽  
Synthesis Method ◽  
Parallel Manipulators ◽  
Rigid Bodies ◽  
Kinematic Chains ◽  
Moving Platforms ◽  
Moving Platform ◽  
Limb Structure

A conventional parallel manipulator is characterized by connecting one moving platform with two or more serial kinematic limbs. Since each limb is independently supporting one moving platform, the moving platform must be a rigid body with several kinematic pairs fixed on it. However, for generalized parallel manipulators with articulated moving platforms, the moving platforms are not limited to rigid bodies but including serial kinematic chains or internal kinematic joints. The introduction of articulated moving platforms allows for improving the kinematic performance of generalized parallel manipulators, especially for rotational capability. On account of the structural characteristics of the moving platforms, it also poses a significant challenge in the construction of the structures of manipulators. This research raises a new method for the type synthesis of generalized parallel manipulators with novel articulated moving platforms. The proposed method introduces a striking shortcut for the limb structure analysis of mechanisms with high rotational capability. In this paper, a class of generalized parallel manipulator with different degrees of freedom from 3 to 6 are constructed by using the constraint synthesis method, and several examples are provided to demonstrate the feasibility of the advocated method. At last, the 3T3R generalized parallel manipulator is taken as an example to analyze the inverse kinematics, and the evaluation of the workspace is conducted to verify the rotational capacity.

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.

An Approach for Acceleration Analysis of Lower Mobility Parallel Manipulators

2011 ◽  
Vol 3 (1) ◽  
Author(s):  
Haitao Liu ◽  
Tian Huang ◽  
Derek G. Chetwynd
Keyword(s):  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Unified Framework ◽  
Generalized Jacobian ◽  
New Approach ◽  
Kinematic Chains ◽  
Lower Mobility ◽  
Acceleration Analysis ◽  
Definition Of ◽  
Closure Constraints

This paper presents a new approach to the velocity and acceleration analyses of lower mobility parallel manipulators. Building on the definition of the “acceleration motor,” the forward and inverse velocity and acceleration equations are formulated such that the relevant analyses can be integrated under a unified framework that is based on the generalized Jacobian. A new Hessian matrix of serial kinematic chains (or limbs) is developed in an explicit and compact form using Lie brackets. This idea is then extended to cover parallel manipulators by considering the loop closure constraints. A 3-PRS parallel manipulator with coupled translational and rotational motion capabilities is analyzed to illustrate the generality and effectiveness of this approach.

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.

Dexterous Workspace of n-PRRR Planar Parallel Manipulators

2012 ◽  
Vol 4 (3) ◽  
Author(s):  
André Gallant ◽  
Roger Boudreau ◽  
Marise Gallant
Keyword(s):  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Divergence Theorem ◽  
End Effector ◽  
Kinematic Chains ◽  
Prismatic Joint ◽  
Planar Surfaces ◽  
Revolute Joints ◽  
Gauss Divergence Theorem ◽  
Planar Parallel Manipulators

In this work, a method is presented to geometrically determine the dexterous workspace boundary of kinematically redundant n-PRRR (n-PRRR indicates that the manipulator consists of n serial kinematic chains that connect the base to the end-effector. Each chain is composed of two actuated (therefore underlined) joints and two passive revolute joints. P indicates a prismatic joint while R indicates a revolute joint.) planar parallel manipulators. The dexterous workspace of each nonredundant RRR kinematic chain is first determined using a four-bar mechanism analogy. The effect of the prismatic actuator is then considered to yield the workspace of each PRRR kinematic chain. The intersection of the dexterous workspaces of all the kinematic chains is then obtained to determine the dexterous workspace of the planar n-PRRR manipulator. The Gauss divergence theorem applied to planar surfaces is implemented to compute the total dexterous workspace area. Finally, two examples are shown to demonstrate applications of the method.

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