Analytical Procedure Based on the Matrix Structural Method for the Analysis of the Stiffness of the 2PRU–1PRS Parallel Manipulator

Robotica ◽  
2019 ◽  
Vol 37 (08) ◽  
pp. 1401-1414
Author(s):  
Saioa Herrero ◽  
Charles Pinto ◽  
Mikel Diez ◽  
Javier Corral
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Shaking Table ◽  
Structural Method ◽  
Positioning Accuracy ◽  
Serial Manipulators ◽  
Kinematic Chains ◽  
Workspace Analysis ◽  
The Matrix

SummaryParallel manipulators, especially those with outputs as one translation and two rotations (1T2R), are being increasingly studied. The kinematic chains of parallel manipulators share the loads and make the stiffness higher than the stiffness of serial manipulators with equivalent limbs. This high stiffness ensures a minimal deformation of the limbs, allowing a high positioning accuracy of the endeffector. Thus, it is very important to be able to measure the stiffness in parallel manipulators. In this work, we present a novel 1T2R multi-axial shaking table (MAST) for automobile pieces testing purposes—the 2PRU–1PRS parallel manipulator—and focus on the analysis of its stiffness all over the useful workspace. Analysis methods based on matrix structural method need to be validated for every parallel manipulator, and we present these steps along with a comparison between experimental and analytical methods.

Workspace Analysis and Going through Singularities of 5-Bar Symmetric Planar Parallel Manipulator by Automated Selective Actuation Mechanism

2012 ◽  
Vol 588-589 ◽  
pp. 1664-1668
Author(s):  
Syam Sundar ◽  
Vijay S. Rathore ◽  
Manoj K. Sahi ◽  
V. Upendran ◽  
Anjan Kumar Dash
Keyword(s):  
Closed Form ◽  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
New Approach ◽  
Serial Manipulators ◽  
Actuation Mechanism ◽  
Geometric Conditions ◽  
Workspace Analysis ◽  
Planar Parallel Manipulator ◽  
Planar Parallel Manipulators

In this article‚ a new approach is presented to determine the various shapes of workspaces of 5 bar symmetric planar parallel manipulators. Here the shape of the workspace is determined by the number of ways the workspaces of the two serial manipulators intersect with each other. Geometric conditions are established in each case and area of each shape of workspace is determined in closed form. Singularity is another important consideration in the design of parallel manipulators. In this paper, an approach is presented to go through the singularity points using an automatic selective actuation mechanism. A prototype 5-bar planar manipulator is fabricated along with an automatic selective actuation mechanism demonstrating the manipulator going through the singularity points.

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.

Experimental Results of a 3-DOF Parallel Manipulator as an Earthquake Motion Simulator

2004 ◽  
Author(s):  
Erika Ottaviano ◽  
Marco Ceccarelli ◽  
Gianni Castelli
Keyword(s):  
Parallel Manipulator ◽  
Linear Acceleration ◽  
Parallel Manipulators ◽  
Experimental Results ◽  
Civil Structures ◽  
Serial Manipulators ◽  
Earthquake Motion ◽  
Motion Simulator ◽  
Earthquake Effects ◽  
New Applications

Parallel manipulators are increasingly used in new applications by exploiting their better characteristics with respect to those of serial manipulators, such as higher stiffness, velocity and acceleration, payload. In this paper, experimental results are presented of a novel application of a 3-DOF CaPaMan (Cassino Parallel Manipulator) prototype to simulate point seismograms and 3D earthquake motion. The rigid body acceleration (linear acceleration, angular velocity and acceleration) has been experimentally analyzed to simulate real 3D earthquakes by using the parallel manipulator. Furthermore, first experimental results are reported to analyze earthquake effects on scaled civil structures.

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.

Considering the Ability for Nonsingular Transitions of Assembly Mode for Dimensional Synthesis

2009 ◽  
Author(s):  
Oscar Altuzarra ◽  
Vi´ctor Petuya ◽  
Mo´nica Uri´zar ◽  
Alfonso Herna´ndez
Keyword(s):  
Parallel Manipulator ◽  
Analytical Procedure ◽  
Parallel Manipulators ◽  
Dimensional Synthesis ◽  
Complex Singularity ◽  
Algebraic Expressions ◽  
Free Region ◽  
Dimensional Parameters ◽  
Cusp Points ◽  
Singularity Locus

An important difficulty in the design of parallel manipulators is their reduced practical workspace, due mainly to the existence of a complex singularity locus within the workspace. The workspace is divided into singularity-free regions according to assembly modes and working modes, and the dimensioning of parallel manipulators aims at the maximization of those regions. It is a common practice to restrict the manipulator’s motion to a specific singularity-free region. However, a suitable motion planning can enlarge the operational workspace by means of transitions of working mode and/or assembly mode. In this paper, the authors present an analytical procedure for obtaining the loci of cusp points of a parallel manipulator as algebraic expressions of its dimensional parameters. The purpose is to find an optimal design for non-singular transitions to be possible.

Motion Performance Analysis of Double-Cylinder Parallel Manipulators

2009 ◽  
Author(s):  
Hong Zhou ◽  
Shehu T. Alimi ◽  
Aravind Ravindranath ◽  
Hareesh Vepuri
Keyword(s):  
Performance Analysis ◽  
Parallel Manipulator ◽  
Critical Role ◽  
Parallel Manipulators ◽  
Degree Of Freedom ◽  
Serial Manipulators ◽  
Operation Speed ◽  
Transmission Angle ◽  
Motion Performance ◽  
Two Degree Of Freedom

Double-cylinder parallel manipulators are closed-loop two-degree-of-freedom linkages. They are preferred to use because of their simplicity plus the common advantages of parallel manipulators such as high stiffness, load-bearing, operation speed and precision positioning. Like other parallel manipulators, the output motion of double-cylinder parallel manipulators is not as flexible as two-degree-of-freedom serial manipulators. The motion performance analysis plays a critical role for this type of parallel manipulator to be applied successfully. In this paper, the linkage feasibility conditions are established based on the transmission angle. When feasibility conditions are satisfied, there is no dead position during operation. The workspace is generated by using curve-enveloping theory. The singularity characteristics are analyzed within the workspace. The motion performance index contours within the workspace are produced using the condition number of the manipulator Jacobian matrix. The results of this paper provide guidelines to apply this type of parallel manipulator.

The differential calculus of screws: Theory, geometrical interpretation, and applications

2009 ◽  
Vol 223 (6) ◽  
pp. 1449-1468 ◽  
Author(s):  
J J Cervantes-Sánchez ◽  
J M Rico-Martínez ◽  
G González-Montiel ◽  
E J González-Galván
Keyword(s):  
Differential Calculus ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Higher Order ◽  
Abstract Concepts ◽  
Serial Manipulators ◽  
Kinematic Chains ◽  
Finite Displacements ◽  
Typical Shape ◽  
Derivatives Of

This article presents a novel and original formula for the higher-order time derivatives, and also for the partial derivatives of screws, which are successively computed in terms of Lie products, thus leading to the automation of the differentiation process. Through the process and, due to the pure geometric nature of the derivation approach, an enlightening physical interpretation of several screw derivatives is accomplished. Important applications for the proposed formula include higher-order kinematic analysis of open and closed kinematic chains and also the kinematic synthesis of serial and parallel manipulators. More specifically, the existence of a natural relationship is shown between the differential calculus of screws and the Lie subalgebras associated with the expected finite displacements of the end effector of an open kinematic chain. In this regard, a simple and comprehensible methodology is obtained, which considerably reduces the abstraction level frequently required when one resorts to more abstract concepts, such as Lie groups or Lie subalgebras; thus keeping the required mathematical background to the extent that is strictly necessary for kinematic purposes. Furthermore, by following the approach proposed in this article, the elements of Lie subalgebra arise in a natural way — due to the corresponding changes in screws through time — and they also have the typical shape of the so-called ordered Lie products that characterize those screws that are compatible with the feasible joint displacements of an arbitrary serial manipulator. Finally, several application examples — involving typical, serial manipulators — are presented in order to prove the feasibility and validity of the proposed method.

scholarly journals Inverse kinematic analysis of 3 DOF 3-PRS PM for machining on inclined prismatic surfaces

2020 ◽  
Vol 9 (2) ◽  
pp. 135
Author(s):  
Hishantkumar Rashmikantbhai Patel ◽  
Yashavant Patel
Keyword(s):  
Parallel Manipulator ◽  
Parallel Manipulators ◽  
Industrial Applications ◽  
Inverse Kinematic ◽  
Medical Surgery ◽  
Space Technology ◽  
Serial Manipulators ◽  
Part Surface ◽  
Primary Focus ◽  
Structural Architecture

<p>Parallel Manipulators (PMs) are family members of modern manipulators based on the closed loop structural architecture. 3-PRS (prismatic, revolute, spherical) manipulator with 3DOF is investigated for its machining capability on prismatic surfaces as it possesses greater structural stiffness, higher pay load caring capacity, more precision compare to serial manipulators as well as less accumulation of errors at joints within a constrained workspace. The said manipulator can be utilized in various fields of application such as precise manufacturing, medical surgery, space technology and many more. In this paper, the primary focus on usage of parallel manipulator in industrial applications such as drilling and grooving on inclined work part surface. Inverse kinematic solutions are used for drilling, square and round profiles on inclined surface using parallel manipulator.</p>

scholarly journals Kinematic Synthesis and Analysis of the RoboMech Class Parallel Manipulator with Two Grippers

Robotics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 99
Author(s):  
Zhumadil Baigunchekov ◽  
Med Amine Laribi ◽  
Azamat Mustafa ◽  
Abzal Kassinov
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Geometric Parameters ◽  
Geometric Constraints ◽  
Least Square ◽  
Kinematic Synthesis ◽  
Serial Manipulators ◽  
Kinematic Chains ◽  
End Effectors ◽  
Cold Stamping

In this paper, methods of kinematic synthesis and analysis of the RoboMech class parallel manipulator (PM) with two grippers (end effectors) are presented. This PM is formed by connecting two output objects (grippers) with a base using two passive and one negative closing kinematic chains (CKCs). A PM with two end effectors can be used for reloading operations of stamped products between two adjacent main technologies in a cold stamping line. Passive CKCs represent two serial manipulators with two degrees of freedom, and negative CKC is a three-joined link with three negative degrees of freedom. A negative CKC imposes three geometric constraints on the movements of the two output objects. Geometric parameters of the negative CKC are determined on the basis of the problems of the Chebyshev and least-square approximations. Problems of positions and analogues of velocities and accelerations of the PM with two end effectors have been solved.

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.

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