Session: MR-02-01 - Theoretical & Computational Kinematics (A.T. Yang Symposium)

Paper Number: 88781

88781 - Higher-Order Kinematics of Lower-Pair Chains With Hyper-Multidual Algebra 

The development of high-precision robotic systems, artificial vision systems, and molecular dynamics, new space docking procedures, require procedures to calculate higher-order accelerations. The key to the proposed approach starts with the property of rigid body displacements group of forming a Lie group, accompanied by its Lie algebra. A previous result offers an isomorphic representation of the Lie group SE (3) with the group of the orthogonal dual tensors and Lie algebra se (3) of the Lie algebra of dual vectors. The results obtained using dual algebras completely solve the problem of finding the field of higher-order accelerations, using a set of results obtained by the previous papers. A  general method for studying the vector field of arbitrary higher-order accelerations is described. It is proved that all information regarding the properties of the distribution of high order accelerations is contained in the specified hyper-multidual (HMD) tensor. The equations that allow the determination of higher-order accelerations are given for the spatial serial kinematic chains. The results are closed-form and coordinate-free. Furthermore, higher-order kinematics properties of lower-pair serial chains with HMD algebra are proposed. The velocities, accelerations, jerks, and jounces fields are offered for an mC general manipulator. The results interest the theoretical kinematics, higher-order kinematics analysis in the case of a serial manipulator, control theory, and multibody kinematics. The development of high-precision robotic systems, artificial vision systems, and molecular dynamics, new space docking procedures, require procedures to calculate higher-order accelerations. The key to the proposed approach starts with the property of rigid body displacements group of forming a Lie group, accompanied by its Lie algebra. A previous result offers an isomorphic representation of the Lie group SE (3) with the group of the orthogonal dual tensors and Lie algebra se (3) of the Lie algebra of dual vectors. The results obtained using dual algebras completely solve the problem of finding the field of higher-order accelerations, using a set of results obtained by the previous papers. A  general method for studying the vector field of arbitrary higher-order accelerations is described. It is proved that all information regarding the properties of the distribution of high order accelerations is contained in the specified hyper-multidual (HMD) tensor. The equations that allow the determination of higher-order accelerations are given for the spatial serial kinematic chains. The results are closed-form and coordinate-free. Furthermore, higher-order kinematics properties of lower-pair serial chains with HMD algebra are proposed. The velocities, accelerations, jerks, and jounces fields are offered for an mC general manipulator. The results interest the theoretical kinematics, higher-order kinematics analysis in the case of a serial manipulator, control theory, and multibody kinematics.

Presenting Author: Daniel Condurache Technical University of Iasi

Presenting Author Biography: Professor Daniel Condurache<br/><br/>Head of Department of <br/>Theoretical Mechanics, &lt;Gheorghe Asachi&gt; Technical University in Iasi, Romania<br/>1990 - Ph.D. in Mathematics<br/>1995 - Ph.D. in Mechanical Engineering <br/><br/>Over 160 papers published in International Journals and then books<br/><br/>Affiliations<br/>- Member of AAS<br/>- Senior Member AIAA<br/>- Member AMS<br/>- Senior Member IEEE<br/>- Member ASME <br/><br/>Areas of interest: <br/>- Astrodynamics<br/>- Dynamical Systems<br/>- Hypercomplex Analysis <br/>- Geometric Algebra

Authors:

Daniel Condurache Technical University of Iasi