Finite Motion Analysis of Parallel Mechanisms with Parasitic Motions Based on Conformal Geometric Algebra

2018 ◽  
Vol 28 (1) ◽  
Author(s):  
Xinming Huo ◽  
Yimin Song
Keyword(s):  
Motion Analysis ◽  
Geometric Algebra ◽  
Conformal Geometric Algebra ◽  
Parallel Mechanisms ◽  
Finite Motion

Forward Kinematics of 3-RPS Parallel Mechanisms Using Conformal Geometric Algebra

2017 ◽  
Author(s):  
Ying Zhang ◽  
Qizheng Liao ◽  
Shimin Wei ◽  
Duanling Li
Keyword(s):  
Geometric Algebra ◽  
Solution Process ◽  
Kinematic Chain ◽  
Polynomial Equation ◽  
Solution Procedure ◽  
Conformal Geometric Algebra ◽  
Forward Kinematics ◽  
Parallel Mechanisms ◽  
Mathematics Mechanization ◽  
Rotational Angle

In this paper, we propose a novel solution process for the forward kinematics of general 3-RPS parallel mechanisms based on conformal geometric algebra (CGA). First of all, the position of one of the three spherical joints is expressed in the rotational angle about the axis of one kinematic chain RPS. Secondly, the other two spherical joints can be determined by this angle via CGA operation. Thirdly, an explicit 16th-degree univariate polynomial equation is reduced from two geometric constraint equations. At last, one numerical example is employed to verify the solution procedure. The novelties of this paper lie in that (1) the modeling formulation and the elimination procedure have intrinsic geometric intuition due to the use of CGA and (2) the 16th-degree polynomial equation without extraneous roots is explicitly formulated and suitable for implementing the mathematics mechanization of this problem.

Foundations for Strip Adjustment of Airborne Laserscanning Data with Conformal Geometric Algebra

2021 ◽  
Vol 32 (1) ◽  
Author(s):  
Eckhard Hitzer ◽  
Werner Benger ◽  
Manfred Niederwieser ◽  
Ramona Baran ◽  
Frank Steinbacher
Keyword(s):  
Geometric Algebra ◽  
Conformal Geometric Algebra

Real-time rendering under distant illumination with conformal geometric algebra

2017 ◽  
Vol 41 (11) ◽  
pp. 4131-4147 ◽  
Author(s):  
Margarita Papaefthymiou ◽  
George Papagiannakis
Keyword(s):  
Real Time ◽  
Geometric Algebra ◽  
Conformal Geometric Algebra

Feature preserving multiresolution subdivision and simplification of point clouds: A conformal geometric algebra approach

2017 ◽  
Vol 41 (11) ◽  
pp. 4074-4087 ◽  
Author(s):  
Shuai Yuan ◽  
Shuai Zhu ◽  
Dong-Shuang Li ◽  
Wen Luo ◽  
Zhao-Yuan Yu ◽  
...  
Keyword(s):  
Geometric Algebra ◽  
Point Clouds ◽  
Conformal Geometric Algebra ◽  
Algebra Approach ◽  
Feature Preserving

Robust Pose Control of Robot Manipulators Using Conformal Geometric Algebra

2014 ◽  
Vol 24 (2) ◽  
pp. 533-552 ◽  
Author(s):  
L. González-Jiménez ◽  
O. Carbajal-Espinosa ◽  
A. Loukianov ◽  
E. Bayro-Corrochano
Keyword(s):  
Geometric Algebra ◽  
Robot Manipulators ◽  
Conformal Geometric Algebra ◽  
Pose Control
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