Projective geometric theorem proving with Grassmann–Cayley algebra

2010 ◽  
pp. 275-285
Author(s):  
Hongbo Li
Keyword(s):  
Theorem Proving ◽  
Geometric Theorem ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra

Combining Clifford Algebraic Computing and Term-Rewriting for Geometric Theorem Proving

1999 ◽  
Vol 39 (1,2) ◽  
pp. 85-104 ◽  
Author(s):  
Stéphane Fèvre ◽  
Dongming Wang
Keyword(s):  
Theorem Proving ◽  
Term Rewriting ◽  
Geometric Theorem ◽  
Algebraic Computing

A geometric approach for singularity analysis of 3-DOF planar parallel manipulators using Grassmann–Cayley algebra

Robotica ◽  
2015 ◽  
Vol 35 (3) ◽  
pp. 511-520 ◽  
Author(s):  
Kefei Wen ◽  
TaeWon Seo ◽  
Jeh Won Lee
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Geometric Approach ◽  
Parallel Manipulators ◽  
Singularity Analysis ◽  
Singular Configurations ◽  
Cayley Algebra ◽  
Grassmann Cayley Algebra ◽  
Planar Parallel Manipulators

SUMMARYSingular configurations of parallel manipulators (PMs) are special poses in which the manipulators cannot maintain their inherent infinite rigidity. These configurations are very important because they prevent the manipulator from being controlled properly, or the manipulator could be damaged. A geometric approach is introduced to identify singular conditions of planar parallel manipulators (PPMs) in this paper. The approach is based on screw theory, Grassmann–Cayley Algebra (GCA), and the static Jacobian matrix. The static Jacobian can be obtained more easily than the kinematic ones in PPMs. The Jacobian is expressed and analyzed by the join and meet operations of GCA. The singular configurations can be divided into three classes. This approach is applied to ten types of common PPMs consisting of three identical legs with one actuated joint and two passive joints.

Automated Reducible Geometric Theorem Proving and Discovery by Gröbner Basis Method

2016 ◽  
Vol 59 (3) ◽  
pp. 331-344 ◽  
Author(s):  
Jie Zhou ◽  
Dingkang Wang ◽  
Yao Sun
Keyword(s):  
Theorem Proving ◽  
Gröbner Basis ◽  
Grobner Basis ◽  
Geometric Theorem ◽  
Basis Method
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