A Method for Determining and Correcting Robot Position and Orientation Errors Due to Manufacturing

1988 ◽  
Vol 110 (1) ◽  
pp. 3-10 ◽  
Author(s):  
P. L. Broderick ◽  
R. J. Cipra
Keyword(s):  
Closed Form Solution ◽  
Difficult Problem ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Correct Position ◽  
Forward Solution ◽  
Simple Task ◽  
Position And Orientation ◽  
Robot Position ◽  
Kinematic Solution

A method is presented for calibration of a robot to correct position and orientation errors due to manufacturing. The method is based on the shape matrix robot kinematic description. Each joint is individually and successively moved in order to explicitly calculate the shape matrix of each link. In addition, methods to correct for the errors in both the forward and inverse kinematic solutions are presented. The modification of the forward solution is a simple task. The modification of the inverse kinematic solution is a difficult problem and is achieved by an iterative technique which supplements the closed-form solution. An example of the calibration and inverse solution is presented to show the improvement in the accuracy of the robot.

Closed-Form Inverse Kinematic Analysis of Variable-Geometry Truss Manipulators

1992 ◽  
Vol 114 (3) ◽  
pp. 438-443 ◽  
Author(s):  
B. Padmanabhan ◽  
V. Arun ◽  
C. F. Reinholtz
Keyword(s):  
Closed Form ◽  
Kinematic Analysis ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Variable Geometry ◽  
Inverse Kinematic Problem ◽  
Inverse Kinematic Analysis ◽  
Variable Geometry Truss

A variety of applications for variable-geometry truss manipulators (VGTMs) have been demonstrated or proposed in the literature. Most of these applications require solution to the inverse kinematic problem, yet only a few isolated examples of closed-form solution methods have been presented to date. This paper provides an overview to the general problem of inverse kinematic analysis of variable-geometry truss manipulators and presents new closed-form solution techniques for problems of practical importance.

Polynomial Inverse Kinematic Solution of the Jaco Robot

2014 ◽  
Author(s):  
Clément Gosselin ◽  
Hanwei Liu
Keyword(s):  
Polynomial Solution ◽  
Solution Process ◽  
Inverse Kinematic ◽  
Degree Polynomial ◽  
Inverse Kinematic Problem ◽  
End Effector ◽  
Numerical Examples ◽  
Position And Orientation ◽  
Kinematic Solution

This article presents a polynomial solution to the inverse kinematic problem of the 6R serial Jaco robot. The solution is specifically tailored to the Jaco robot, which is not wrist-partitioned. The derivation of the univariate 16-degree polynomial is presented, starting from the direct kinematic equations providing the position and orientation of the end-effector as a function of the joint variables. Upon calculation of the roots of the polynomial, all joint variables are obtained by backsubstitution, leading to a unique set of joint variables for each of the roots. Also, it is shown that for certain configurations, the 16-degree polynomial contains only terms of even powers while all terms are not zero in general. Two numerical examples are given to demonstrate the effectiveness of the solution process.

Closed Form Solution to Workspace of Hexapod-Based Virtual Axis Machine Tools

1999 ◽  
Vol 121 (1) ◽  
pp. 26-31 ◽  
Author(s):  
T. Huang ◽  
J. Wang ◽  
D. J. Whitehouse
Keyword(s):  
Machine Tools ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mobile Platform ◽  
Unified Framework ◽  
Closed Solution ◽  
Workspace Analysis ◽  
Position And Orientation ◽  
First Time ◽  
Workspace Boundary

A novel methodology is presented in this paper for the workspace analysis of virtual axis machine tools. The workspace is defined which enables to describe in a unified framework both the position and orientation capabilities of the mobile platform. Given a range of the orientation of the mobile platform, the piecewise closed solution to the workspace boundary is formulated. It is indicated for the first time that the workspace boundary in fact is the cap of twelve envelope surfaces. Two examples are given to illustrate the effectiveness of this approach.

3D Modeling and Closed-Form Inverse Kinematics Solution for 6dof Surgical Robot

2013 ◽  
Vol 455 ◽  
pp. 533-538
Author(s):  
Edris Farah ◽  
Shao Gang Liu
Keyword(s):  
Closed Form ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Surgical Robot ◽  
Decoupling Method ◽  
Six Degrees Of Freedom ◽  
Inverse Kinematics Problem

Since robots began to inter the medical fields, more research efforts and more attention have been given to this kind of robots. In this paper six degrees of freedom surgical robot was studied. The Denavit-Hartenberg parameters of the robot have been computed and 3D model has been built by using open source robotics toolbox. The paper also discussed a closed form solution for the inverse kinematics problem by using inverse kinematic decoupling method.

Dual quaternion-based inverse kinematics of the general spatial 7R mechanism

2008 ◽  
Vol 222 (8) ◽  
pp. 1593-1598 ◽  
Author(s):  
D Gan ◽  
Q Liao ◽  
S Wei ◽  
J S Dai ◽  
S Qiao
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Dual Quaternion ◽  
Whole Process ◽  
Inverse Kinematic Analysis ◽  
Angular Displacements ◽  
Output Equation ◽  
Theoretical Results

The theory of dual quaternion and its use in serial mechanisms are described in this paper. A closed-form solution to the inverse kinematic analysis of the general 7-link 7R mechanism is presented. Dixon's resultant is used and the input—output equation is expressed in the form of a 6×6 determinant equated to zero, and the formulae to determine other angular displacements are expressed in the closed form. Numerical example confirms these theoretical results. The whole process is very simple and easy to program, which supplies a new method for the real use of the 7R mechanism.

scholarly journals Decoupled Closed-Form Solution for Humanoid Lower Limb Kinematics

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Alejandro Said ◽  
Ernesto Rodriguez-Leal ◽  
Rogelio Soto ◽  
J. L. Gordillo ◽  
Leonardo Garrido
Keyword(s):  
Closed Form ◽  
Lower Limb ◽  
Closed Form Solution ◽  
Numerical Data ◽  
Geometric Approach ◽  
Form Solution ◽  
Experimental Implementation ◽  
Limb Kinematics ◽  
Position And Orientation ◽  
Lower Limb Kinematics

This paper presents an explicit, omnidirectional, analytical, and decoupled closed-form solution for the lower limb kinematics of the humanoid robot NAO. The paper starts by decoupling the position and orientation analysis from the overall Denavit-Hartenberg (DH) transformation matrices. Here, the joint activation sequence for the DH matrices is based on the geometry of a triangle. Furthermore, the implementation of a forward and a reversed kinematic analysis for the support and swing phase equations is developed to avoid matrix inversion. The allocation of constant transformations allows the position and orientation end-coordinate systems to be aligned with each other. Also, the redefinition of the DH transformations and the use of constraints allow decoupling the shared DOF between the legs and the torso. Finally, a geometric approach to avoid the singularities during the walking process is indicated. Numerical data is presented along with an experimental implementation to prove the validity of the analytical results.

An Analysis of Adhesive-Bonded Single-Lap Joints

1983 ◽  
Vol 50 (1) ◽  
pp. 109-115 ◽  
Author(s):  
Du Chen ◽  
Shun Cheng
Keyword(s):  
High Stress ◽  
Closed Form Solution ◽  
Adhesive Layer ◽  
Energy Functional ◽  
Difficult Problem ◽  
Lap Joints ◽  
Form Solution ◽  
Adhesive Layers ◽  
Single Lap Joints ◽  
Constant Coefficients

Because of the technical importance and difficulty of the analysis, the present problem has been treated, as seen in the literature, by a number of authors. In the current paper a unified method is presented that has advantages in several respects for the analysis of this difficult problem and may also be employed for solving other similar problems. The method is based on two-dimensional elasticity theory in conjunction with the variational principal of complementary energy. Minimizing the energy functional leads to two coupled, fourth-order ordinary differential equations with constant coefficients for the determination of the stresses. By means of the present approach, a closed-form solution, which is adaptable for any possible adhesive layer flexibility and capable of satisfying all the boundary stress conditions of the joint, is obtained. To illustrate the application of the present unified theory, three typical examples for flexible, medium, and inflexible adhesive layers are provided and comparisons are made among these examples and with other known solutions. Special attention is given to the stress distribution in the end zones where high stress intensities of the joints occur.

Design and Construction of a Statically-Balanced Direct Drive ARM

1987 ◽  
Author(s):  
H. Kazerooni ◽  
S. Kim
Keyword(s):  
Closed Form ◽  
Robot Manipulator ◽  
Impedance Control ◽  
Closed Form Solution ◽  
Inverse Kinematic ◽  
Form Solution ◽  
Direct Drive ◽  
University Of Minnesota ◽  
Closed Form Solutions ◽  
The University

Abstract A statically-balanced direct drive robot manipulator is being constructed at the University of Minnesota for analysis of manufacturing tasks such as deburrlng and grinding when Impedance Control (8, 10, 11) is used to control the robot. This mechanism using a four bar linkage is designed without extra counterweights. As a result of elimination of the gravity forces on the drive system, smaller actuators (and consequently smaller amplifiers) are chosen to guarantee the acceleration of about 5g without overheating the motors. This mechanism results in closed-form solution for Inverse kinematics. The closed-form solutions for dynamic and Inverse kinematic have been derived. High torque, low speed brush-less AC synchronous motors are used to power the robot. The relatively “large” workspace of this configuration is suitable for manufacturing tasks. Graphite epoxy composite material is being used for the construction of the robot links.

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