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.

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.

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.

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.

Displacement Analysis of the 3SPS-3CCS Mechanism Based on Hyper-Chaotic Damp Least Square Method

2011 ◽  
Vol 55-57 ◽  
pp. 2092-2098
Author(s):  
You Xin Luo ◽  
Qi Yuan Liu ◽  
Xiao Yi Che ◽  
Bin Zeng
Keyword(s):  
Mathematical Model ◽  
Real Number ◽  
Matrix Method ◽  
Parallel Mechanism ◽  
Least Square Method ◽  
Least Square ◽  
Forward Displacement ◽  
Displacement Analysis ◽  
Chaotic Sequences ◽  
Chaos System

The forward displacement analysis of parallel mechanism is attributed to find the solutions of complicated nonlinear equations and it is a very difficult process. Taking chaotic sequences as the initial values of the damp least square method, we can find all the solutions of equations quickly. Making use of existing chaos system and discovering new chaos system to generate chaotic sequences with good properties is the key to the damp least square method based on Chaos sequences. Based on utilizing hyper-chaotic Hénon mapping to obtain initial points, a new method of finding all real number solutions of the nonlinear questions is proposed. Using cosine matrix method, the author established the mathematical model of forward displacement for the generalized 3SPS-3CCS parallel robot mechanism and a numerical example is given. Compared to the quaternion method building mathematical model, the result shows cosine matrix method building mathematical model and hyper-chaotic damp least square method to find solution is brief and high calculation efficiency as the calculation is done in real number range. The proposed method has universality which can be used in forward displacement of other parallel mechanism.

Sign in / Sign up

Export Citation Format

Share Document