Design and kinematic analysis of a rotary positioner

Robotica ◽  
2006 ◽  
Vol 25 (1) ◽  
pp. 75-85 ◽  
Author(s):  
Borys Shchokin ◽  
Farrokh Janabi-Sharifi
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Stewart Platform ◽  
Optimal Combination ◽  
Variable Length ◽  
Mobile Platform ◽  
Constant Length ◽  
Forward And Inverse Kinematics ◽  
Circular Base

A rotary positioner (RP) is a type of parallel manipulator that is similar to a Stewart Platform. Instead of having variable-length bars, however, an RP has constant-length limbs located between a mobile platform as well as six circular motors distributed on a circular base. This paper offers a detailed investigation of an RP, focusing on its mechanism and analyzing its forward and inverse kinematics. It also computes an RP's constant orientation and orientation workspaces, taking into account the constraints imposed by passive joints and links interference. The optimal combination of the main parameters for an RP's maximum possible translation and orientation is also provided.

Kinematics and Dynamics of a Parallel Manipulator With Woven Joints

1993 ◽  
Author(s):  
Hyunsok Pang
Keyword(s):  
Lagrange Multipliers ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Numerical Technique ◽  
Vector Analysis ◽  
Kinematics And Dynamics ◽  
Governing Equations ◽  
Numerical Examples

Abstract Presented is an analysis of the kinematics and the inverse dynamics of a proposed three DOF parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangin technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers in order to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline.

An Algebraic Method for Direct Position Analysis of the General Stewart Platform Manipulator Robot

2009 ◽  
Vol 626-627 ◽  
pp. 405-410
Author(s):  
Xi Guang Huang ◽  
Guang Pin He ◽  
Q.Z. Liao
Keyword(s):  
Parallel Manipulator ◽  
Algebraic Method ◽  
Stewart Platform ◽  
Mobile Platform ◽  
Analysis Problem ◽  
Position Analysis ◽  
General Geometry ◽  
Six Degree Of Freedom ◽  
Manipulator Robot ◽  
Base Platform

Stewart platform manipulator robot is a six degree of freedom, parallel manipulator, which consists of a base platform, a mobile platform and six limbs connected at six distinct points on the base platform and the mobile platform respectively. The direct position analysis problem of Stewart platform relates to the determination of the mobile platform pose for a given set of the lengths of the limbs. In this paper, we present a concise algebraic method for solving the direct position analysis problem for the fully parallel manipulator with general geometry, often referred to as General Stewart platform manipulator. Based on the presented algebraic method, we derive a 40th degree univariate polynomial from a determinant of 20×20 Sylvester’s matrix, which is relatively small in size. We also obtain a complete set of 40 solutions to the most general Stewart platform. The proposed method is comparatively concise and reduces the computational burden. Finally the method is demonstrated by a numerical example.

A Study on the Kinematics of 2-DOF Parallel Manipulator

2011 ◽  
Vol 148-149 ◽  
pp. 1487-1490
Author(s):  
Jong Gyu Lee ◽  
Sang Ryong Lee ◽  
Choon Young Lee ◽  
Seung Han Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Displacement Velocity ◽  
Linear Motion ◽  
End Effector ◽  
Verification Algorithm

In this paper, a parallel manipulator is comprised of sliders and links. The end-effector has an orientation. Sliders execute a linear motion along parallel guidelines and make the connected links rotate. We derived displacement, velocity and acceleration from kinematic analysis of this manipulator using direct and inverse kinematics,found constraint conditions and proposed the verification algorithm of constraint conditions. With the result from the simulation, we found that there was a local workspace where the manipulator cannot carry out a series of link motion.

Kinematics of a n–bay triangle–triangle variable geometry truss manipulator

Robotica ◽  
1992 ◽  
Vol 10 (3) ◽  
pp. 263-267
Author(s):  
L. Beiner
Keyword(s):  
Iterative Method ◽  
Closed Form ◽  
Inverse Kinematics ◽  
Variable Length ◽  
Variable Geometry ◽  
Closed Form Solutions ◽  
Numerical Example ◽  
Forward And Inverse Kinematics ◽  
Variable Geometry Truss Manipulator ◽  
Variable Geometry Truss

SUMMARYVariable geometry truss manipulators (VGTM) are static trusses where the lengths of some members can be varied, allowing one to control the position of the free end relative to the fixed one. This paper deals with a planar VGTM consisting of a n–bay triangle-triangle truss with one variable length link (i.e. one DOF) per bay. Closed-form solutions to the forward, inverse, and velocity kinematics of a 3-DOF version of this VGTM are presented, while the forward and inverse kinematics of an n–DOF (redundant) one are solved by a recursive and an iterative method, respectively. A numerical example is presented.

scholarly journals Kinematics, Structural Analysis and Control of 3-PPSS Parallel Manipulator

2019 ◽  
Vol 8 (6S4) ◽  
pp. 911-916
Keyword(s):  
Structural Analysis ◽  
Kinematic Analysis ◽  
Parallel Manipulator ◽  
Low Cost ◽  
Inverse Kinematic ◽  
Mobile Platform ◽  
Ansys Software ◽  
Marquardt Algorithm ◽  
Prismatic Joints ◽  
And Control

CIndustries encourage the use of low-cost compact and easily controllable equipment’s to implement automation due to the lack of skilled labors and low productivity. This demands the need for more efficient and affordable novel mechanisms and processes. In this paper, the kinematic analysis of a 3-PPSS (P— prismatic joint, S- spherical joint) parallel manipulator having an equilateral mobile platform is explained. The Kinematic analysis is done using the Modified Denavit-Hartenberg (DH) modelling technique. The inverse kinematic equations are further solved using Levenberg-Marquardt Algorithm to obtain an exact solution for the joint variables corresponding to an instantaneous pose of the end effector. Static structural analysis is done using ANSYS software to determine the deformations and stresses induced. Optimum dimensions are chosen for the manipulator based on this analysis. Finally, an ARDUINO based control is implemented to manipulate the mobile platform by controlling the active prismatic joints.

Mechanical Design and Kinematic Analysis of a Three-Legged Six Degree-of-Freedom Parallel Manipulator

1992 ◽  
Author(s):  
D. Zlatanov ◽  
M. Q. Dai ◽  
R. G. Fenton ◽  
B. Benhabib
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Mechanical Design ◽  
Closed Form Solution ◽  
Form Solution ◽  
Forward Kinematics ◽  
Spherical Joint ◽  
Revolute Joints ◽  
Forward And Inverse Kinematics ◽  
Six Degree Of Freedom

Abstract In this paper a three-legged 6-dof platform-type parallel manipulator is described. Each of the legs is a serial subchain with three revolute joints connected to the output platform via a spherical joint. Due to the proposed asymmetrical 3-2-1 distribution of the controlled joints, a closed-form solution exists to the forward kinematics problem. The mechanical design of the manipulator has been developed. The forward and inverse kinematics as well as the instantaneous kinematics of the mechanism have been solved analytically.

Kinematic analysis and testing of a 6-RRRPRR parallel manipulator

2016 ◽  
Vol 231 (13) ◽  
pp. 2515-2527 ◽  
Author(s):  
Yang Yu ◽  
Zhen-bang Xu ◽  
Qing-wen Wu ◽  
Peng Yu ◽  
Shuai He ◽  
...  
Keyword(s):  
Kinematic Analysis ◽  
Software Package ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Ball Screw ◽  
Helical Motion ◽  
Automotive Applications ◽  
Vector Method ◽  
Parasitic Motion ◽  
Accuracy And Repeatability

The Gough-Stewart platform has been successfully used in a wide variety of fields ranging from medical to automotive applications. This paper proposes a 6-RR RPRR parallel manipulator with orthogonal non-intersecting RR-joint configurations and ball screw actuators without guide mechanisms. A novel methodology is developed to define the dependent RR-joint variables and a numerical algorithm is employed to calculate the joint variables. The parasitic motion caused by the helical motion of the ball screw can be expressed and solved with vector method. The inverse kinematics of this manipulator can be solved. To verify the effectiveness of the proposed approach, simulations are performed with software package ADAMS. A prototype of this manipulator is manufactured. Its resolution, accuracy, and repeatability are measured. It is shown that the presented method is effective for this parallel manipulator.

scholarly journals Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

Robotics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 31
Author(s):  
Alexey Fomin ◽  
Anton Antonov ◽  
Victor Glazunov ◽  
Yuri Rodionov
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Forward Kinematics ◽  
Rotational Angle ◽  
End Effector ◽  
Kinematic Chains ◽  
Position And Orientation ◽  
Manipulator Design ◽  
Forward Kinematic

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

Inverse Kinematic and Dynamic Analyses of the 6-UCU Parallel Manipulator

2011 ◽  
Vol 127 ◽  
pp. 172-180 ◽  
Author(s):  
Guo Jun Liu ◽  
Shu Tao Zheng ◽  
Peter O. Ogbobe ◽  
Jun Wei Han
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Driving Forces ◽  
Stewart Platform ◽  
Inverse Kinematic ◽  
Euler Method ◽  
Kinematics And Dynamics ◽  
Precise Analysis ◽  
Dynamic Analyses ◽  
Reaction Forces

From the practical viewpoint, the inverse kinematics and dynamics of a practical Stewart platform, the 6-UCU parallel manipulator, are established in this paper. The velocities and accelerations of the manipulator are derived with the consideration of the attachments of the joints, and then the driving forces actuated by the actuators and the reaction forces applied to the joints are derived based on the Newton Euler method. In the last, the correctness of the equations established in this paper is confirmed by the study of a case. These equations can be used as the base for the precise analysis of the 6-UCU parallel manipulator.

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