Inverse Kinematics of General 4R2P, 3R3P, 4R1C, 2R2C, and 3C Serial Manipulators

1992 ◽  
Author(s):  
Dilip Kohli ◽  
Michael Osvatic
Keyword(s):  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Serial Manipulators ◽  
Linearly Independent ◽  
The Matrix ◽  
Half Angle ◽  
Inverse Kinematics Problem ◽  
Joint Variable ◽  
General Geometry ◽  
Solution Methodology

Abstract This paper presents a solution to the inverse kinematics problem for 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators of general geometry. The method used to solve these is based on a technique recently presented by the authors for solving the inverse kinematics of general 6R and 5R1P manipulators. In the 6R and 5R1P cases, the method initially starts using 14 linearly independent equations where as for the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulator only 3, 6, 7 or 10 linearly independent equations are required, depending on the case. Through the use of a linearization and dialytic elimination method all 4R2P, 3R3P, 4R1C, 2R2C and 3C cases are reduced to equating to zero the determinant of a matrix whose elements are linear in the tangent of a half angle of a joint variable. The size of this matrix is (8 × 8) for all 4R2P manipulators, (2 × 2) for all 3R3P and 3C manipulators, (16 × 16) for 4R1C manipulators, (4 × 4) for RCRC and CRCR manipulators and (8 × 8) for the remaining 2R2C manipulators providing 8th, 2nd, 16th, 4th and 8th degree inverse kinematic polynomial respectively. Thus, the determinant equated to zero gives us the characteristic equation of the degree expected. The unique form of the matrix allows us to obtain the solution by solving an eigenvalue problem. Many variations of the 4R2P, 3R3P, 4R1C, 2R2C and 3C manipulators are presented and the solution methodology is illustrated by several numerical examples.

A Method of Inverse Kinematics Solution for a Class of Robotic Manipulators

1997 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Nonlinear Equation ◽  
Analytical Method ◽  
Multiple Solutions ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Singular Configurations ◽  
Inverse Kinematics Problem ◽  
Joint Variable

Abstract A semi-analytical method and a computer program are developed for inverse kinematics solution of a class of robotic manipulators, in which four joint variables are contained in wrist point equations. For this case, it becomes possible to express all the joint variables in terms of a joint variable, and this reduces the inverse kinematics problem to solving a nonlinear equation in terms of that joint variable. The solution can be obtained by iterative methods and the remaining joint variables can easily be computed by using the solved joint variable. Since the method is manipulator dependent, the equations will be different for kinematically different classes of manipulators, and should be derived analytically. A significant benefit of the method is that, the singular configurations and the multiple solutions indicated by sign ambiguities can be determined while deriving the inverse kinematic expressions. The developed method is applied to a six-revolute-joint industrial robot, FANUC Arc Mate Sr.

Inverse Kinematic Solution of Robot Manipulators Using Interval Analysis

1998 ◽  
Vol 120 (1) ◽  
pp. 147-150 ◽  
Author(s):  
R. S. Rao ◽  
A. Asaithambi ◽  
S. K. Agrawal
Keyword(s):  
Computational Complexity ◽  
Numerical Algorithm ◽  
Interval Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Real Numbers ◽  
Computational Mathematics ◽  
All Solutions ◽  
Inverse Kinematics Problem ◽  
Kinematic Solution

Interval analysis is a growing branch of computational mathematics where operations are carried out on intervals instead of real numbers. This paper presents the first application of this method to robotic mechanisms for the solution of inverse kinematics. As shown in this paper, it is possible to potentially compute all solutions of the inverse kinematics problem using this method. This paper describes the preliminaries of interval analysis, the numerical algorithm, the computational complexity, and illustrations with examples.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Lu Bing Hang ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Algebraic Method ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Parallel Mechanisms ◽  
Simple Method ◽  
Inverse Kinematics Problem ◽  
Serial Robot

Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on one-dimension searching algorithm. The new method has the following features: (1) Using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

A Simple Method for Inverse Kinematic Analysis of the General 6R Serial Robot

2006 ◽  
Vol 129 (8) ◽  
pp. 793-798 ◽  
Author(s):  
Shi Zhi Xin ◽  
Luo Yu Feng ◽  
Hang Lu Bing ◽  
Yang Ting Li
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
New Method ◽  
One Dimension ◽  
Forward Kinematics ◽  
The Real ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Inverse Kinematic Analysis

The inverse kinematic analysis of the general 6R serial robot has been a very significant and important problem in the theory of the spatial mechanisms. Because the solution to inverse kinematics problem of the general 5R serial robot is unique and its assembly condition has been derived, a simple effective method for inverse kinematics problem of general 6R serial robot or forward kinematics problem of general 7R single-loop mechanism is presented based on a one-dimension searching algorithm. All the real solutions to inverse kinematics problems of the general 6R serial robot or forward kinematics problems of the general 7R single-loop mechanism can be obtained. The new method has the following features: (1) using one-dimension searching algorithm, all the real inverse kinematic solutions are obtained and it has higher computing efficiency; and (2) compared with the algebraic method, it has evidently reduced the difficulty of deducing formulas. The principle of the new method can be generalized to kinematic analysis of parallel mechanisms.

Determining the Number of Inverse Kinematic Solutions of a Constrained Parallel Mechanism Using a Homotopy Algorithm

2010 ◽  
Vol 2 (2) ◽  
Author(s):  
Jeremy T. Newkirk ◽  
Layne T. Watson ◽  
Michael M. Stanišić
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Shoulder Girdle ◽  
Inverse Kinematic ◽  
Variable Length ◽  
Real Solutions ◽  
Homotopy Algorithm ◽  
Fixed Length ◽  
Multivalued Solution ◽  
Inverse Kinematics Problem

This paper numerically determines the number of real-valued inverse kinematic solutions to a constrained parallel mechanism composed of three triangular platforms. The base and middle platforms are connected by three fixed-length legs, while the middle and distal platforms are connected by three variable length legs that extend out of the fixed-length legs in a collinear fashion. All legs are connected to the platforms via spherical joints at the corners. This mechanism is intended to replicate the motion of a human shoulder girdle. The constrained parallel mechanism has a multivalued solution to the inverse kinematics problem. A homotopy method was used to numerically compute the inverse kinematic solutions for over 100 cases. Each case was filtered for the number of real-valued solutions. The maximum number of real solutions was found to be 8, but in some cases there were fewer solutions.

An Analytical Inverse Kinematics Solution Method for Robotic Manipulators

2000 ◽  
Author(s):  
Tuna Balkan ◽  
M. Kemal Özgören ◽  
M. A. Sahir Arikan ◽  
H. Murat Baykurt
Keyword(s):  
Inverse Kinematics ◽  
Industrial Robot ◽  
Robotic Manipulators ◽  
Inverse Kinematic ◽  
Industrial Robots ◽  
Solution Approach ◽  
Joint Variable ◽  
Forward Kinematic ◽  
Six Degree Of Freedom ◽  
Kinematic Solution

Abstract In this study, an inverse kinematic solution approach applicable to six degree-of-freedom industrial robotic manipulators is introduced. The approach is based on a previously introduced kinematic classification of industrial robotic manipulators by Balkan et al. (1999), and depending on the kinematic structure, either an analytical or a semi-analytical inverse kinematic solution is obtained. The semi-analytical method is named as the parametrized joint variable (PJV) method. Compact forward kinematic equations obtained by utilizing the properties of exponential rotation matrices. In the inverse kinematic solutions of the industrial robots surveyed in the previous study, most of the simplified compact equations can be solved analytically and the remaining few of them can be solved semi-analytically through a numerical solution of a single univariate equation. In these solutions, the singularities and the multiple configurations of the manipulators can be determined easily. By the method employed in this study, the kinematic and inverse kinematic analysis of any manipulator or designed-to-be manipulator can be performed and using the solutions obtained, the inverse kinematics can also be computerized by means of short and fast algorithms. As an example for the demonstration of the applicability of the presented method to manipulators with closed-chains, ABB IRB2000 industrial robot is selected which has a four-bar mechanism for the actuation of the third link, and its compact forward kinematic equations are given as well as the inverse kinematic solution.

On the Placement of Serial Manipulators

2000 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu
Keyword(s):  
Cost Function ◽  
Inverse Kinematics ◽  
Inverse Kinematic ◽  
Working Environment ◽  
Robot Arm ◽  
Serial Manipulators ◽  
Surface Patches ◽  
Numerical Formulation ◽  
Fixed Reference ◽  
Position And Orientation

Abstract Criteria and implementation for the placement robot manipulators with the objective to reach specified target points are herein addressed. Placement of a serial manipulator in a working environment is characterized by defining the position and orientation of the manipulator’s base with respect to a fixed reference frame. The problem has become of importance in both the medical and manufacturing fields, where a robot arm must be appropriately placed with respect to targets that cannot be moved. A broadly applicable numerical formulation is presented. While other methods have used inverse kinematics solutions in their formulation for defining a locality for the manipulator base, this type of solution is difficult to implement because of the inherent complexities in determining al inverse kinematic solutions. The approach taken in this work is based on characterizing the placement forcing a cost function to impel the workspace envelope in terms of surface patches towards the target points and subject to functionality constraints, but that does not require the computation of inverse kinematics. The formulation and experimental code are demonstrated using a number of examples.

Proper Smart Method of the Inverse Kinematic Problem

2015 ◽  
Vol 772 ◽  
pp. 455-460 ◽  
Author(s):  
Adrian Olaru ◽  
Serban Olaru ◽  
Niculae Mihai
Keyword(s):  
Inverse Kinematics ◽  
Jacobian Matrix ◽  
Inverse Kinematic ◽  
Iterative Approximation ◽  
Inverse Kinematic Problem ◽  
Space Curves ◽  
Inverse Kinematics Problem ◽  
Artificial Intelligence Algorithm ◽  
Pseudo Inverse

One of the most precise method solving the inverse kinematics problem in the redundant cases of the robots is the coupled method. The proposed method use the Iterative Pseudo Inverse Jacobian Matrix Method (IPIJMM) coupled with the proper Sigmoid Bipolar Hyperbolic Tangent Neural Network with Time Delay and Recurrent Links (SBHTNN-TDRL). One precise solution of the inverse kinematics problem is very difficult to find, when the degree of freedom increase and in many cases this is impossible because the redundant solutions. In all these cases must be used the numerical iterative approximation, like the proposed method, with artificial intelligence algorithm. The paper describe all the steps in one case study to obtain the space circle curve in different planes by using one arm type robot and the proposed method. The errors of the space movement of the robot end-effecter, after applying the proposed method, was less than 0,01. The presented method is general and it can be used in all other robots types and for all other conventional and unconventional space curves.

Inverse Kinematics of Serial-Chain Manipulators

1996 ◽  
Vol 118 (3) ◽  
pp. 396-404 ◽  
Author(s):  
Hong-You Lee ◽  
Charles F. Reinholtz
Keyword(s):  
Inverse Kinematics ◽  
Minimum Degree ◽  
Complete Solution ◽  
Linear Equations ◽  
End Effector ◽  
Serial Chain ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomials ◽  
General Geometry

This paper proposes a unified method for the complete solution of the inverse kinematics problem of serial-chain manipulators. This method reduces the inverse kinematics problem for any 6 degree-of-freedom serial-chain manipulator to a single univariate polynomial of minimum degree from the fewest possible closure equations. It is shown that the univariate polynomials of 16th degree for the 6R, 5R-P and 4R-C manipulators with general geometry can be derived from 14, 10 and 6 closure equations, respectively, while the 8th and 4th degree polynomials for all the 4R-2P, 3R-P-C, 2R-2C, 3R-E and 3R-S manipulators can be derived from only 2 closure equations. All the remaining joint variables follow from linear equations once the roots of the univariate polynomials are found. This method works equally well for manipulators with special geometry. The minimal properties may provide a basis for a deeper understanding of manipulator geometry, and at the same time, facilitate the determination of all possible configurations of a manipulator with respect to a given end-effector position, the determination of the workspace and its subspaces with the different number of configurations, and the identification of singularity positions of the end-effector. This paper also clarifies the relationship between the three known solutions of the general 6R manipulator as originating from a single set of 14 equations by the first author.

Application of Dual-Number Matrices to the Inverse Kinematics Problem of Robot Manipulators

1985 ◽  
Vol 107 (2) ◽  
pp. 201-208 ◽  
Author(s):  
G. R. Pennock ◽  
A. T. Yang
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Robot Manipulators ◽  
Closed Form Solutions ◽  
Dual Number ◽  
Special Geometry ◽  
Inverse Kinematics Problem ◽  
Concise Representation ◽  
Joint Parameters ◽  
General Geometry

This paper presents the application of dual-number matrices to the formulation of displacement equations of robot manipulators with completely general geometry. Dual-number matrices make possible a concise representation of link proportions and joint parameters; together with the orthogonality properties of the matrices we are able to derive, in a systematic manner, closed-form solutions for the joint displacements of robot manipulators with special geometry as illustrated by three examples. It is hoped that the method presented here will provide a meaningful alternative to existing methods for formulating the inverse kinematics problem of robot manipulators.

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