Real-Time Forward Position Kinematics of the Spatial Parallel Manipulator

2013 ◽  
Vol 712-715 ◽  
pp. 2241-2248
Author(s):  
Jian Wei Mi ◽  
Li Du ◽  
Xue Chao Duan
Keyword(s):  
Real Time ◽  
High Precision ◽  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Time Algorithm ◽  
Initial Position ◽  
End Effector ◽  
Time Consumption ◽  
Online Implementation

Aiming at online implementation, a real-time algorithm for forward position kinematics of the parallel manipulators is proposed, in which the steepest decent direction of the solution iteration is constructed with Jacobian matrix, with the initial position for iteration arbitrarily chosen from the workspace. Under the condition of motion continuity of the end-effector, the unique forward position kinematics solution can be found out with this algorithm. Forward position kinematics case studies of spatial parallel manipulators were conducted, which show that the algorithm has the advantages of a high precision, little iteration and less millisecond-level time consumption.

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.

Dynamic modeling, system identification and comparative study of various control strategies for a spatial parallel manipulator

2021 ◽  
pp. 095965182110320
Author(s):  
Mervin Joe Thomas ◽  
Shoby George ◽  
Deepak Sreedharan ◽  
ML Joy ◽  
AP Sudheer
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Control Strategies ◽  
Proportional Integral Derivative ◽  
Real Time Control ◽  
Model Predictive Controller ◽  
End Effector ◽  
Proportional Integral ◽  
Time Control ◽  
Predictive Controller

The significant challenges seen with the mathematical modeling and control of spatial parallel manipulators are its difficulty in the kinematic formulation and the inability to real-time control. The analytical approaches for the determination of the kinematic solutions are computationally expensive. This is due to the passive joints, solvability issues with non-linear equations, and inherent kinematic constraints within the manipulator architecture. Therefore, this article concentrates on an artificial neural network–based system identification approach to resolve the complexities of mathematical formulations. Moreover, the low computation time with neural networks adds up to its advantage of real-time control. Besides, this article compares the performance of a constant gain proportional–integral–derivative (PID), variable gain proportional–integral–derivative, model predictive controller, and a cascade controller with combined variable proportional–integral–derivative and model predictive controller for real-time tracking of the end-effector. The control strategies are simulated on the Simulink model of a 6-degree-of-freedom 3-PPSS (P—prismatic; S—spherical) parallel manipulator. The simulation and real-time experiments performed on the fabricated manipulator prototype indicate that the proposed cascade controller with position and velocity compensation is an appropriate method for accurate tracking along the desired path. Also, training the network using the experimentally generated data set incorporates the mechanical joint approximations and link deformities present in the fabricated model into the predicted results. In addition, this article showcases the application of Euler–Lagrangian formalism on the 3-PPSS parallel manipulator for its dynamic model incorporating the system constraints. The Lagrangian multipliers include the influence of the constraint forces acting on the manipulator platform. For completeness, the analytical model results have been verified using ADAMS for a pre-defined end-effector trajectory.

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.

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.

scholarly journals Singularity Conditions of 3T1R Parallel Manipulators With Identical Limb Structures

2012 ◽  
Vol 4 (1) ◽  
Author(s):  
Semaan Amine ◽  
Mehdi Tale Masouleh ◽  
Stéphane Caro ◽  
Philippe Wenger ◽  
Clément Gosselin
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Type Synthesis ◽  
Constraint Analysis ◽  
Fixed Direction ◽  
Geometric Singularity ◽  
Grassmann Geometry ◽  
Grassmann Cayley Algebra

This paper deals with the singularity analysis of parallel manipulators with identical limb structures performing Schönflies motions, namely, three independent translations and one rotation about an axis of fixed direction (3T1R). Eleven architectures obtained from a recent type synthesis of such manipulators are analyzed. The constraint analysis shows that these architectures are all overconstrained and share some common properties between the actuation and the constraint wrenches. The singularities of such manipulators are examined through the singularity analysis of the 4-RUU parallel manipulator. A wrench graph representing the constraint wrenches and the actuation forces of the manipulator is introduced to formulate its superbracket. Grassmann–Cayley Algebra is used to obtain geometric singularity conditions. Based on the concept of wrench graph, Grassmann geometry is used to show the rank deficiency of the Jacobian matrix for the singularity conditions. Finally, this paper shows the general aspect of the obtained singularity conditions and their validity for 3T1R parallel manipulators with identical limb structures.

Unified Solving Jacobian∕Hessian Matrices of Some Parallel Manipulators With n SPS Active Legs and a Passive Constrained Leg

2006 ◽  
Vol 129 (11) ◽  
pp. 1161-1169 ◽  
Author(s):  
Yi Lu ◽  
Bo Hu
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Hessian Matrix ◽  
Parallel Manipulators ◽  
Simple Approach ◽  
Spherical Joint ◽  
Load Bearing ◽  
Prismatic Joint ◽  
First Order ◽  
Partial Differentiation

Some parallel manipulators with n spherical joint-prismatic joint-spherical joint (SPS)-type active legs and a passive constrained leg possess a larger capability of load bearing and are simple in structure of the active leg. In this paper, a unified and simple approach is proposed for solving Jacobian∕Hessian matrices and inverse∕forward velocity and acceleration of this type of parallel manipulators. First, a general parallel manipulator with n SPS-type active legs and one passive constrained leg in various possible serial structure is synthesized, and some formulae for solving the poses of constrained force∕torque and active∕constrained force matrix are derived. Second, the formulae for solving extension of active legs, the auxiliary velocity∕acceleration equation are derived. Third, the formulae for solving inverse∕forward velocity and acceleration and a Jacobian matrix without the first-order partial differentiation and a Hessian matrix without the second-order partial differentiation are derived. Finally, the procedure is applied to three parallel manipulators with four and five SPS-type active legs and one passive constrained leg in different serial structures and to illustrate.

A new family of spherical parallel manipulators

Robotica ◽  
2002 ◽  
Vol 20 (4) ◽  
pp. 353-358 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
End Effector ◽  
Singular Configurations ◽  
New Family ◽  
Geometric Conditions ◽  
Singularity Locus ◽  
The Given ◽  
Spherical Parallel Manipulator ◽  
Spherical Motion

In the literature, 3-RRPRR architectures were proposed to obtain pure translation manipulators. Moreover, the geometric conditions, which 3-RRPRR architectures must match, in order to make the end-effector (platform) perform infinitesimal (elementary) spherical motion were enunciated. The ability to perform elementary spherical motion is a necessary but not sufficient condition to conclude that the platform is bound to accomplish finite spherical motion, i.e. that the mechanism is a spherical parallel manipulator (parallel wrist). This paper demonstrates that the 3-RRPRR architectures matching the geometric conditions for elementary spherical motion make the platform accomplish finite spherical motion, i.e. they are parallel wrists (3-RRPRR wrist), provided that some singular configurations, named translation singularities, are not reached. Moreover, it shows that 3-RRPRR wrists belong to a family of parallel wrists which share the same analytic expression of the constraints which the legs impose on the platform. Finally, the condition that identifies all the translation singularities of the mechanisms of this family is found and geometrically interpreted. The result of this analysis is that the translation singularity locus can be represented by a surface (singularity surface) in the configuration space of the mechanism. Singularity surfaces drawn by exploiting the given condition are useful tools in designing these wrists.

Two Natural Dexterity Indices for Parallel Manipulators: Angularity and Axiality

2014 ◽  
Vol 6 (4) ◽  
Author(s):  
J. Jesús Cervantes-Sánchez ◽  
J. M. Rico-Martínez ◽  
V. H. Pérez-Muñoz
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Mobile Platform ◽  
Angular Velocity Vector ◽  
Motion Sensitivity ◽  
Physical Insight ◽  
Dimensionally Homogeneous Jacobian Matrix ◽  
The One ◽  
General Motion

This paper introduces two novel dexterity indices, namely, angularity and axiality, which are used to estimate the motion sensitivity of the mobile platform of a parallel manipulator undergoing a general motion involving translation and rotation. On the one hand, the angularity index can be used to measure the sensitivity of the mobile platform to change in rotation. On the other hand, the axiality index can be used to measure the sensitivity of the operation point (OP) of the mobile platform to change in translation. Since both indices were inspired by very fundamental concepts of classical kinematics (angular velocity vector and helicoidal velocity field), they offer a clear and simple physical insight, which is expected to be meaningful to the designer of parallel manipulators. Moreover, the proposed indices do not require obtaining a dimensionally homogeneous Jacobian matrix, nor do they depend on having similar types of actuators in each manipulator's leg. The details of the methodology are illustrated by considering a classical parallel manipulator.

An optimal singularity-free motion planning method for a 6-DOF parallel manipulator

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shiqi Li ◽  
Dong Chen ◽  
Junfeng Wang
Keyword(s):  
Particle Swarm Optimization ◽  
Motion Planning ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Free Motion ◽  
Motion Path ◽  
Swarm Optimization ◽  
End Effector ◽  
Content Type ◽  
Multi Objective

Purpose This paper aims to present a method of optimal singularity-free motion planning under multiple objectives and multiple constrains for the 6-DOF parallel manipulator, which is used as an execution mechanism for the automated docking of components. Design/methodology/approach First, the distribution characteristics of the Jacobian matrix determinant in local workspace are studied based on the kinematics and a sufficient and necessary condition of singularity-free path planning in local workspace is proposed. Then, a singularity-free motion path of the end-effector is generated by a fifth-order B-spline curve and the corresponding trajectories of each actuator are obtained via the inverse kinematics. Finally, several objective functions are defined to evaluate the motion path and an improved multi-objective particle swarm optimization algorithm-based on the Pareto archive evolution is developed to obtain the optimal singularity-free motion trajectories. Findings If the initial pose and the target pose of the end-effector are both singularity-free, a singularity-free motion path can be planned in the local workspace as long as all the values of each pose elements in their own directions are monotonous. The improved multi-objective particle swarm optimization (IMPSO) algorithm is effective and efficient in the optimization of multi-objective motion planning model. The optimal singularity-free motion path of the end-effector is verified in the component docking test. The docking result is that the movable component is in alignment with the fixed one, which proves the feasibility and practicability of the proposed motion path method to some extent. Originality/value The proposed method has a certain novelty value in kinematic multi-objective motion planning of parallel manipulators; it also increases the application prospect of parallel manipulators and provides attractive solutions to component assembly for those organizations with limited cost and that want to find an option that is effective to be implemented.

Kinematics and Singularity Analysis of the Hexaglide Parallel Robot

2008 ◽  
Author(s):  
Mansour Abtahi ◽  
Hodjat Pendar ◽  
Aria Alasty ◽  
Gholamreza Vossoughi
Keyword(s):  
Machine Tools ◽  
Parallel Manipulator ◽  
High Speed ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Parallel Robot ◽  
Singularity Analysis ◽  
The Past ◽  
Different Types ◽  
Forward Kinematic

In the past few years, parallel manipulators have become increasingly popular in industry, especially, in the field of machine tools. Hexaglide is a 6 DOF parallel manipulator that can be used as a high speed milling machine. In this paper, the kinematics and singularity of Hexaglide parallel manipulator are studied systematically. At first, this robot has been modeled and its inverse and forward kinematic problems have been solved. Then, formulas for solving inverse velocity are derived and Jacobian matrix is obtained. After that, three different types of singularity for this type of robot have been investigated. Finally a numerical example is presented.

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