TY - GEN
T1 - Computer aided synthesis of piecewise rational motions for planar 2R and 3R robot arms
AU - Jin, Zhe
AU - Ge, Q. J.
PY - 2006
Y1 - 2006
N2 - This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. The paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that the problem of synthesizing the Cartesian rational motion of a planar 2R arm can be reduced to that of circular interpolations in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a planar 3R arm can be reduced to that of circular interpolation in one plane and constrained spline interpolation in a circular ring. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated. For applications that require C2 continuous motions, the paper presents a joint-space based method for generating a C2 continuous motion that approximates a given C1 rational motion of the end link.
AB - This paper deals with the problem of synthesizing piecewise rational motions of an object that satisfies kinematic constraints imposed by a planar robot arm with revolute joints. The paper brings together the kinematics of planar robot arms and the recently developed freeform rational motions to study the problem of synthesizing constrained rational motions for Cartesian motion planning. Through the use of planar quaternions, it is shown that the problem of synthesizing the Cartesian rational motion of a planar 2R arm can be reduced to that of circular interpolations in two separate planes. Furthermore, the problem of synthesizing the Cartesian rational motion of a planar 3R arm can be reduced to that of circular interpolation in one plane and constrained spline interpolation in a circular ring. Due to the limitation of circular interpolation, only C1 continuous rational motions are generated. For applications that require C2 continuous motions, the paper presents a joint-space based method for generating a C2 continuous motion that approximates a given C1 rational motion of the end link.
UR - https://www.scopus.com/pages/publications/33751347111
U2 - 10.1115/detc2006-99649
DO - 10.1115/detc2006-99649
M3 - Conference contribution
AN - SCOPUS:33751347111
SN - 079183784X
SN - 9780791837849
T3 - Proceedings of the ASME Design Engineering Technical Conference
BT - Proceedings of 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006
PB - American Society of Mechanical Engineers
T2 - 2006 ASME International Design Engineering Technical Conferences and Computers and Information In Engineering Conference, DETC2006
Y2 - 10 September 2006 through 13 September 2006
ER -