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.

Analytic Form Solution of the Direct Position Analysis of a Wide Family of Three-Legged Parallel Manipulators

2005 ◽  
Vol 128 (1) ◽  
pp. 264-271 ◽  
Author(s):  
Raffaele Di Gregorio
Keyword(s):  
Analytic Form ◽  
Parallel Manipulators ◽  
Analytical Form ◽  
Form Solution ◽  
Kinematic Chains ◽  
Position Analysis ◽  
In Series ◽  
The One ◽  
Generic Structures ◽  
Wide Family

A wide family of parallel manipulators (PMs) is the one that groups all 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. Two out of these topologies are the SR-2PS topology (one SR leg and two PS legs) and the SP-2RS topology (one SP leg and two RS legs). This paper presents two algorithms. The first one determines all the assembly modes of the SR-2PS structures. The second one determines all the assembly modes of the SP-2RS structures. The presented algorithms can be applied without changes to solve, in analytical form, the direct position analysis (DPA) of all the parallel manipulators that generate a SR-2PS structure or a SP-2RS structure when the actuators are locked. In particular, the closure equations of two generic structures, one of type SR-2PS and the other of type SP-2RS, are written. The eliminants of the two systems of equations are determined and the solution procedures are presented. Finally, the proposed procedures are applied to real cases. This work demonstrates that (i) the DPA solutions of any PM that becomes a SR-2PS structure are at most eight, and (ii) the DPA solutions of any PM that becomes a SP-2RS structure are at most sixteen.

Position Analysis in Analytical Form of the 3-PSP Mechanism

1999 ◽  
Vol 123 (1) ◽  
pp. 51-55 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Nonlinear Equations ◽  
Parallel Mechanism ◽  
Analytical Form ◽  
Rigid Bodies ◽  
The Other ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Fixed Base ◽  
Inverse Position Analysis ◽  
Movable Platform

In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to nonlinear equations that are difficult to solve. In particular, the inverse position analysis comprises different subproblems which need specific solution techniques. Finally a numerical example is reported.

Kinematic analyses of novel translational parallel manipulators

2013 ◽  
Vol 228 (2) ◽  
pp. 330-341 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Horacio Orozco-Mendoza ◽  
Alvaro Sánchez-Rodríguez ◽  
Gursel Alici
Keyword(s):  
Parallel Manipulator ◽  
Screw Theory ◽  
Linear Equations ◽  
Parallel Manipulators ◽  
Output Displacement ◽  
Kinematic Analyses ◽  
Linear Actuators ◽  
The One ◽  
Forward Kinematic ◽  
Primary Contribution

This study reports on the kinematic analyses of four translational parallel manipulators (3RPC, SPS + 2RPC, RPPR + 2RPC and RPPR + 2PPP) articulated with linear actuators. They are based on serially connected chains which are connected with cylindrical (C), prismatic (P), revolute (R), spherical (S) and universal (U) joints. Of these manipulators, the one which is a fully decoupled, fully isotropic and singularity-free translational parallel manipulator (RPPR+2PPP) offers a one-to-one correspondence between its input and output displacement. This makes its forward and inverse position analyses simpler with a set of linear equations to be solved. Although the other manipulators have coupled kinematics, they still have simpler forward kinematic equations over other well-known translational parallel manipulators reported in the literature. We also employ screw theory to undertake the velocity and acceleration analyses. The primary contribution of this manuscript is to show how the 3-RPC translational parallel manipulator can be gradually modified in order to obtain a fully isotropic, fully decoupled and singularity-free translational parallel manipulator.

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.

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.

Position Analysis in Analytical Form of the 3-PSP Mechanism

1999 ◽  
Author(s):  
Raffaele Di Gregorio ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Parallel Mechanism ◽  
Linear Equations ◽  
Analytical Form ◽  
Rigid Bodies ◽  
Kinematic Chains ◽  
Position Analysis ◽  
Fixed Base ◽  
Inverse Position Analysis ◽  
Movable Platform ◽  
Non Linear Equations

Abstract In this paper the direct and the inverse position analysis of a 3-dof fully-parallel mechanism, known as 3-PSP mechanism, is addressed and solved in analytical form. The 3-PSP mechanism consists of two rigid bodies, one movable (platform) and the other fixed (base), connected to each other by means of three equal serial kinematic chains (legs) of type PSP, P and S standing for prismatic and spherical pair respectively. Both the direct and the inverse position analysis of this mechanism lead to non-linear equations that are difficult to solve. In particular, the inverse position analysis comprises different sub-problems which need specific solution techniques. Finally a numerical example is reported.

Kinematics of a 6-DOF parallel manipulator with two limbs actuated by spherical motion generators

2021 ◽  
pp. 095440622110329
Author(s):  
Kun Wang ◽  
Xiaoyong Wu ◽  
Yujin Wang ◽  
Jun Ding ◽  
Shaoping Bai
Keyword(s):  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Practical Application ◽  
Numerical Examples ◽  
Position Analysis ◽  
Kinematic Study ◽  
Small Footprint ◽  
Dual Arm ◽  
Spherical Motion

Inspired by dual-arm-like manipulation, a novel 6-DOF parallel manipulator with two spherical-universal-revolute limbs is proposed. Compared with general 6-DOF parallel manipulators with six limbs, this new manipulator actuated by spherical motion generators has only two limbs, which brings advantages such as fewer active limbs for avoiding interference, larger reachable and orientational workspace for complex operating, more actuators integrated in active modules for decreasing installation errors and increasing compactness. In this paper, the kinematics of this novel parallel manipulator is solved and illustrated, covering its inverse and forward position analysis, workspace and singularities. The kinematic study reveals interesting features of this manipulator such as multiple working and assembly modes, small footprint and large workspace volume with high dexterity. Numerical examples of kinematic analysis are included. Practical application of the new manipulator is illustrated.

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.

Precise Stiffness and Elastic Deformations of Serial–Parallel Manipulators by Considering Inertial Wrench of Moving Links

Robotica ◽  
2020 ◽  
Vol 38 (12) ◽  
pp. 2204-2220
Author(s):  
Yi Lu ◽  
Zhuohong Dai ◽  
Yang Lu
Keyword(s):  
Elastic Deformation ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Elastic Deformations ◽  
In Series ◽  
Deformation Models

SUMMARYA general serial–parallel manipulator connected in series by two different parallel manipulators with linear active legs is constructed. Its precise stiffness and elastic deformations are studied systematically. Its unified precise stiffness and precise elastic deformation models are established by considering both the moving links inertial wrench and the dynamic active/constrained wrench. A 3SPR+3RPS-type serial–parallel manipulator is illustrated for solving its precise stiffness and precise elastic deformation. The derived formulae of the precise stiffness and the precise elastic deformations of the general serial–parallel manipulator are verified by the theoretical solutions of the 3SPR+3RPS serial–parallel manipulator.

A New Algorithm Based on Two Extra-Sensors for Real-Time Computation of the Actual Configuration of the Generalized Stewart-Gough Manipulator

1998 ◽  
Author(s):  
V. Parenti-Castelli ◽  
R. Di Gregorio
Keyword(s):  
Real Time ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Computational Burden ◽  
The Real ◽  
Position Analysis ◽  
Extra Information ◽  
Actual Configuration ◽  
General Geometry

Abstract It is well known that the direct position analysis of fully-parallel manipulators provides more than one solution, i.e., more than one configuration of the mechanism is possible for a given set of the actuated variables of motion. Extra information is, thus, necessary to find the actual configuration of the manipulator. This paper presents a new algorithm for the real-time computation of the actual configuration of the generalized Stewart-Gough manipulator, also known as 6-6 fully-parallel manipulator with general geometry. The proposed algorithm makes use of two extra rotary sensors in addition to the six normally implemented in the servosystems of the manipulator. A one-to-one correspondence between the sensor measurements and the manipulator configuration is provided. With respect to other algorithms recently presented in the literature, the proposed method greatly reduces the computational burden. Finally a case study shows the effectiveness of the proposed procedure.

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