Analysis of Spatial Open-Loop System by Means of Direction Cosine Transformation Matrices

1989 ◽  
Vol 111 (4) ◽  
pp. 508-512 ◽  
Author(s):  
T. C. Yih ◽  
Y. Youm
Keyword(s):  
Industrial Robot ◽  
Direction Cosine ◽  
Open Loop ◽  
Coordinate Systems ◽  
Open Loop System ◽  
Transformation Matrices ◽  
Joint Axis ◽  
Cosine Transformation ◽  
Direction Cosine Matrix ◽  
Unit Vectors

In this paper, an analytical approach for the displacement analysis of spatial openloop systems by means of direction cosine transformation matrices is presented. Two local coordinate systems at each joint are designated to formulate the direction cosine matrices, in recursive form, of the joint axis and link vector. Elements of the 3×3 direction cosine transformation matrices are computed based on the geometry of successive link elements, the unit vectors of preceding joint axis and link vector, and the cofactors of direction cosine matrix. The analysis using direction cosine matrix method will provide the “exact” joint positions in space. A computer algorithm is developed to investigate the workspaces of spatial n-R open-loop systems that projected onto the X-Y, Y-Z, and Z-X coordinate planes, respectively. Numerical examples for the workspaces of an industrial robot and the human upper extremity are illustrated.

On the Displacement Analysis of Open-Loop Systems by the Direction Cosine Matrix Method

1987 ◽  
Author(s):  
Y. Youm ◽  
T. Yih
Keyword(s):  
Matrix Method ◽  
Direction Cosine ◽  
Open Loop ◽  
Open Loop System ◽  
Displacement Analysis ◽  
Transformation Matrices ◽  
Joint Axis ◽  
Cosine Transformation ◽  
Direction Cosine Matrix ◽  
Unit Vectors

Abstract In this paper, displacement analysis of a general spatial open-loop system and a computer algorithm for the workspace of the system are developed by applying the direction cosine matrix method. In using this method, one global coordinate system and two joint local coordinate systems must be predefined in order to formulate the direction cosine transformation matrices of the unit vectors of each joint axis and link vector. The 3 × 3 direction cosine transformation matrices for each joint axis and link vector are established based on the known geometric configurations, the preceding unit vectors, and the cofactor property of the direction cosine matrix. The use of cofactor property will provide a unique solution for the transformation matrix. A computer algorithm is developed to illustrate the workspace of spatial n-R open-loop systems projected onto the coordinate X-Y, Y-Z, and X-Z planes. Numerical examples are demonstrated for an industrial robot, an application to human upper extremity, and a hypothetical 9-link open-loop system.

Exact Displacement Analysis of Four-Link Spatial Mechanisms by the Direction Cosine Matrix Method

1984 ◽  
Vol 51 (4) ◽  
pp. 921-928 ◽  
Author(s):  
T. C. Huang ◽  
Y. Youm
Keyword(s):  
Local Coordinate System ◽  
Direction Cosine ◽  
Displacement Analysis ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Local Coordinates ◽  
Development Direction ◽  
Direction Cosine Matrix ◽  
Direction Cosines ◽  
Unit Vectors

A method of displacement analysis of the four-link spatial mechanism is developed. The results through this analysis will be exact solutions that can be obtained without resorting to numerical or iteration schemes. In the analysis, the position of a link in a mechanism can be fully defined if its direction and length are known. Therefore, this analysis involves the calculation of the unknown direction cosines and length of each link for a given configuration of the mechanism. In finding the direction cosines of the unknown unit vectors involved for each link and rotating axis, two types of coordinates, the global and the local, are generally used. Then, a direction cosine matrix between each local coordinate system and the global coordinates is established. Thus, the unknown direction cosines of the local coordinates, the links, and the rotating axes are obtained in global coordinates. In this development, direction cosine matrices are used throughout the analysis. As an illustration, the application of this method to the study of four-link spatial mechanisms, RGGR, RGCR, RRGG, and RRGC will be presented.

The Method for Solving Kinematics of an Industrial Robot

2013 ◽  
Vol 282 ◽  
pp. 274-281 ◽  
Author(s):  
Lenka Baločková
Keyword(s):  
Industrial Robot ◽  
Kinematic Structure ◽  
Coordinate Systems ◽  
Transformation Matrices ◽  
Basic Transformation ◽  
Direct Kinematics

This article deals with an overview of kinematic structures of industrial operating robots in cartesian, cylindrical, spherical and angular coordinating system. The second half of the article deals with solution of direct kinematics. Each of the coordinate systems is graphically shown and verbally described. Basic transformation matrices are used for the solution of direct kinematics and subsequently the Denavit-Hartenberg method, placing coordinate systems of robotic structure RRRT, is described in details. Calculated workspaces of kinematic structure RRRT are shown at the end of this article.

Attitude reconstruction from strap-down rate gyros using power series

2021 ◽  
pp. 1-19
Author(s):  
Habib Ghanbarpourasl
Keyword(s):  
Power Series ◽  
Taylor Series ◽  
Direction Cosine ◽  
Analytical Description ◽  
Double Precision ◽  
Angular Velocity Vector ◽  
Higher Order Terms ◽  
Direction Cosine Matrix ◽  
The Stability ◽  
Better Than

Abstract This paper introduces a power series based method for attitude reconstruction from triad orthogonal strap-down gyros. The method is implemented and validated using quaternions and direction cosine matrix in single and double precision implementation forms. It is supposed that data from gyros are sampled with high frequency and a fitted polynomial is used for an analytical description of the angular velocity vector. The method is compared with the well-known Taylor series approach, and the stability of the coefficients’ norm in higher-order terms for both methods is analysed. It is shown that the norm of quaternions’ derivatives in the Taylor series is bigger than the equivalent terms coefficients in the power series. In the proposed method, more terms can be used in the power series before the saturation of the coefficients and the error of the proposed method is less than that for other methods. The numerical results show that the application of the proposed method with quaternions performs better than other methods. The method is robust with respect to the noise of the sensors and has a low computational load compared with other methods.

Multi-Stage System Identification of a Gas Turbine

2017 ◽  
Author(s):  
Amit Pandey ◽  
Maurício de Oliveira ◽  
Chad M. Holcomb
Keyword(s):  
Gas Turbine ◽  
Closed Loop ◽  
Open Loop ◽  
Loop System ◽  
Closed Loop Control ◽  
Input Output ◽  
Open Loop System ◽  
Loop Control ◽  
Multi Stage ◽  
Identification Techniques

Several techniques have recently been proposed to identify open-loop system models from input-output data obtained while the plant is operating under closed-loop control. So called multi-stage identification techniques are particularly useful in industrial applications where obtaining input-output information in the absence of closed-loop control is often difficult. These open-loop system models can then be employed in the design of more sophisticated closed-loop controllers. This paper introduces a methodology to identify linear open-loop models of gas turbine engines using a multi-stage identification procedure. The procedure utilizes closed-loop data to identify a closed-loop sensitivity function in the first stage and extracts the open-loop plant model in the second stage. The closed-loop data can be obtained by any sufficiently informative experiment from a plant in operation or simulation. We present simulation results here. This is the logical process to follow since using experimentation is often prohibitively expensive and unpractical. Both identification stages use standard open-loop identification techniques. We then propose a series of techniques to validate the accuracy of the identified models against first principles simulations in both the time and frequency domains. Finally, the potential to use these models for control design is discussed.

Modeling of Multibody Flexible Articulated Structures With Mutually Coupled Motions: Part II — Application and Results

1992 ◽  
Author(s):  
Jiechi Xu ◽  
Joseph R. Baumgarten
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Universal Joint ◽  
Open Loop System ◽  
Numerical Examples ◽  
Kinematic Properties ◽  
Good Agreement

Abstract The application of the systematic procedures in the derivation of the equations of motion proposed in Part I of this work is demonstrated and implemented in detail. The equations of motion for each subsystem are derived individually and are assembled under the concept of compatibility between the local kinematic properties of the elastic degrees of freedom of those connected elastic members. The specific structure under consideration is characterized as an open loop system with spherical unconstrained chains being capable of rotating about a Hooke’s or universal joint. The rigid body motion, due to two unknown rotations, and the elastic degrees of freedom are mutually coupled and influence each other. The traditional motion superposition approach is no longer applicable herein. Numerical examples for several cases are presented. These simulations are compared with the experimental data and good agreement is indicated.

Sign in / Sign up

Export Citation Format

Share Document