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.

Modular Method for Kinematic Analysis of Parallel Manipulators Based on Ordered SOCs

2006 ◽  
Author(s):  
Zhi Xin Shi ◽  
Yu Feng Luo ◽  
Ting Li Yang
Keyword(s):  
Kinematic Analysis ◽  
Continuation Method ◽  
Algebraic Method ◽  
Parallel Manipulators ◽  
New Method ◽  
Homotopy Continuation ◽  
Parallel Mechanisms ◽  
Unknown Variable ◽  
Homotopy Continuation Method ◽  
Modular Method

Based on the new viewpoint of structural decomposion that any multi-loop mechanism are made up of by a series of ordered single opened chains(SOCs), a new method for kinematic analysis of parallel manipulators, i.e, the SOCs modular method has been presented in the paper. The new method has the following features: (1) The dimensions of sets of the nonlinear kinematic analysis equations are reduced to the minimum, and the kinematic analysis equation often contains only one unknown variable for most parallel manipulators generally applied now. Accordingly, all the real solutions to forward kinematics problem of parallel mechanisms can be easily obtained by using one-dimension searching algorithm; (2) Compared with algebraic method, it has evidently reduced the difficulty of deducing formulas; (3) Compared with homotopy continuation method, it has higher computing efficiency.

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 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.

Posture Prediction Versus Inverse Kinematics

2001 ◽  
Author(s):  
Karim Abdel-Malek ◽  
Wei Yu ◽  
Zan Mi ◽  
E. Tanbour ◽  
M. Jaber
Keyword(s):  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Human Performance ◽  
Inverse Kinematic ◽  
Cost Functions ◽  
Optimization Approach ◽  
Final Position ◽  
Serial Robot ◽  
Posture Prediction

Abstract Inverse kinematics is concerned with the determination of joint variables of a manipulator given its final position or final position and orientation. Posture prediction also refers to the same problem but is typically associated with models of the human limbs, in particular for postures assumed by the torso and upper extremities. There has been numerous works pertaining to the determination and enumeration of inverse kinematic solutions for serial robot manipulators. Part of these works have also been directly extended to the determination of postures for humans, but have rarely addressed the choice of solutions undertaken by humans, but have focused on purely kinematic solutions. In this paper, we present a theoretical framework that is based on cost functions as human performance measures, subsequently predicting postures based on optimizing one or more of such cost functions. This paper seeks to answer two questions: (1) Is a given point reachable (2) If the point is reachable, we shall predict a realistic posture. We believe that the human brain assumes different postures driven by the task to be executed and not only on geometry. Furthermore, because of our optimization approach to the inverse kinematics problem, models with large number of degrees of freedom are addressed. The method is illustrated using several examples.

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.

Kinematic Analysis and Digital Mock-up Based Hybrid Verification about the Industrial Robot with Symmetric Dual Planar Four-Bar Mechanism

2012 ◽  
Vol 251 ◽  
pp. 191-195
Author(s):  
Xiao Xi Chen ◽  
Ping He ◽  
Liu Han
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Industrial Robot ◽  
Forward Kinematics ◽  
Kinematic Modeling ◽  
Inverse Kinematics Problem

In this paper, the context of relative kinematic modeling, and the analysis of symmetric dual four-bar mechanism industrial robot are introduced. For such mechanism, its designation of the representative algorithm, and its simplification, simulation, verification and alternately analysis in Forward Kinematics Problems (FKP) and Inverse Kinematics Problem (IKP) were studied. Via such method, it’s possible to efficiently analyze and solve the both of FKP and IKP of symmetric dual planar four-bar mechanism. Thus this method can be applied for the design, simulation and verification for the robot with similar structure.

A Computational Algorithm for a Spatial Serial Robot

2011 ◽  
Vol 217-218 ◽  
pp. 233-237
Author(s):  
Xi Guang Huang
Keyword(s):  
Automatic Control ◽  
Inverse Kinematics ◽  
Computational Algorithm ◽  
Polynomial Equation ◽  
Central Problem ◽  
Serial Robots ◽  
Symbolic Calculations ◽  
Inverse Kinematics Problem ◽  
Serial Robot ◽  
Univariate Polynomial

The inverse kinematics of serial robots is a central problem in the automatic control of robot manipulators. The aim of this paper is to obtain a computational algorithm to compute the inverse kinematics problem of a spatial serial robot. We use a series of algebraic and numeric transformations to reduce the problem to a univariate polynomial equation. The results can be directly applied to symbolic calculations and decreased considerably the calculation time.

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.

Sign in / Sign up

Export Citation Format

Share Document