TY - GEN
T1 - A UNIFIED DESIGN EQUATION TO REPRESENT GEOMETRIC CONSTRAINTS OF SPATIAL SS, ES AND SE DYADS
AU - Deng, Xueting
AU - Purwar, Anurag
AU - Ge, Qiaode Jeffrey
N1 - Publisher Copyright: © 2023 American Society of Mechanical Engineers (ASME). All rights reserved.
PY - 2023
Y1 - 2023
N2 - This paper presents a unified design equation for the type and dimensional synthesis of spatial SS, ES and SE dyads for the motion synthesis problems, where S stands for a spherical and E stands for a planar joint. While there has been a lot of research on dimensional synthesis of planar and spherical mechanisms, little work has been done on the type and dimensional synthesis of spatial mechanisms. In this paper, we show that we can derive a single algebraic equation to represent geometric constraints of each of the SS, ES, and SE spatial dyads. While this design equation represents geometric constraints redundantly, explicit mechanical constraints have to be applied to extract the type and dimensional parameters of dyads during synthesis. A two-step algorithm is used to first algebraically fit the given pose constraints of the moving platform and then constraints are applied to obtain type and dimensions. The algebraic fitting is performed using singular value decomposition and candidate sets of solution vectors are obtained. While these candidate vectors are capable of representing any type of spatial dyads, quadratic constraints are applied to obtain mechanical dyads. This paper is an extension of our previous work on type and dimensional synthesis of planar dyads formed with R (Revolute) and P (Prismatic) joints.
AB - This paper presents a unified design equation for the type and dimensional synthesis of spatial SS, ES and SE dyads for the motion synthesis problems, where S stands for a spherical and E stands for a planar joint. While there has been a lot of research on dimensional synthesis of planar and spherical mechanisms, little work has been done on the type and dimensional synthesis of spatial mechanisms. In this paper, we show that we can derive a single algebraic equation to represent geometric constraints of each of the SS, ES, and SE spatial dyads. While this design equation represents geometric constraints redundantly, explicit mechanical constraints have to be applied to extract the type and dimensional parameters of dyads during synthesis. A two-step algorithm is used to first algebraically fit the given pose constraints of the moving platform and then constraints are applied to obtain type and dimensions. The algebraic fitting is performed using singular value decomposition and candidate sets of solution vectors are obtained. While these candidate vectors are capable of representing any type of spatial dyads, quadratic constraints are applied to obtain mechanical dyads. This paper is an extension of our previous work on type and dimensional synthesis of planar dyads formed with R (Revolute) and P (Prismatic) joints.
KW - Dimensional Synthesis
KW - Dual Quaternion
KW - Motion Synthesis
KW - Singular Value Decomposition
KW - Spatial Mechanism
KW - Type Synthesis
UR - https://www.scopus.com/pages/publications/85178611890
U2 - 10.1115/DETC2023-117282
DO - 10.1115/DETC2023-117282
M3 - Conference contribution
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - 47th Mechanisms and Robotics Conference (MR)
PB - American Society of Mechanical Engineers (ASME)
T2 - ASME 2023 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC-CIE 2023
Y2 - 20 August 2023 through 23 August 2023
ER -