Metric Mobility Criterion of Bricard Trihedral Linkage via the 4D Geometric Algebra

10.6567/IFToMM.14TH.WC.OS8.030

Chung-Ching Lee

Geometric algebra ； Clifford-Grassmann algebra ； dimensional mobility criteria ； Bricard trihedral linkage ； Paradoxical linkage

Proceedings of the 14th IFToMM World Congress

14th-2（2015 / 10 / 27）

515 - 520

英文

Geometric algebra, also called Clifford-Grassmann algebra or hypercomplex number, can deal with space geometric problems in an easy and compact way. Using it to transform three-dimensional (3D) Euclidean geometric entities to actual elements of four-dimensional (4D) geometric algebra (abbreviated to G4), motion displacements are regarded as even elements of G4. Based on the combined rotation and translation in G4, one can establish the metric constraints of movable spatial paradoxical linkages. This paper describes fundamentals of geometric algebra and introduces the composition of two successive finite rotations. Then, a rigid-body motion in G4 is disclosed for a possible application in computational kinematics through the geometric algebra. Finally, the metric or dimensional mobility criterion of Bricard trihedral six-revolute paradoxical linkage is algebraically verified.