This study proposes a new method using Euler parameters and quaternion algebra for the kinematic synthesis of an RRSS spatial motion generator. The proposed method is compared with the other method using rotation angles for two-position and three-position motion guide problems.
It is found that the proposed method provides solutions better in most cases tested here because the synthesis equations in the method include no trigonometric functions. The solutions converge more easily than in the other method as well as avoiding rotational singularity problems encountered otherwise.
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References
1.
SuhC. H.RadcliffeC. W.Kinematics and mechanisms design, 1978 (John Wiley and Sons, New York).
2.
NikraveshP. E.Computer-aided analysis of mechanical systems, 1988 (Prentice-Hall, Englewood Cliffs, New Jersey).
3.
RothB.Finite position theory applied to mechanism synthesis. Trans. ASME J. Appl. Mechanics, 1967, 34(3), 599–605.
4.
SandorG. N.XuY.WengT. C.Synthesis of 7–R spatial motion generators with prescribed crank rotations and elimination of branching. Int. J. Robotics Res., 1986, 5(2), 143–156.
5.
SandorG. N.WengT. C.XuY.The synthesis of spatial motion generators with prismatic, revolute and cylindric pairs without branching defect. Mechanism and Machine Theory, 1988, 23(4), 269–274.
6.
ChiangC. H.ChiengW. H.HoeltzelD. A.Synthesis of the RSCR mechanism for four precision positions with relaxed specifications. Mechanism and Machine Theory, 1992, 27(2), 157–167.
7.
ChiangC. H.ChiengW. H.HoeltzelD. A.Four-position synthesis for spatial mechanisms with two loops. The Twenty-second ASME Mechanisms Conference Scottsdale Arizona, 1992, Vol. 46, Mechanical Design and Synthesis, pp. 499–509 (ASME).
8.
HamiltonW. R.Elements of quaternions, 3rd edition, 1969 (Chelsea Publishing Company, New York).
SpringK. W.Euler parameters and the use of quaternion algebra in the manipulation of finite rotations: a review. Mechanism and Machine Theory, 1986, 21(5), 365–373.
11.
FundaF.TaylorR. H.PaulR. P.On homogeneous transforms, quaternion, and computational efficiency. Trans. IEEE Robotics and Automn, 1990, 6(3), 382–388.
12.
ChouJ. C. K.Quaternion kinematic and dynamic differential equations. Trans. IEEE Robotics and Automn, 1992, 8(1), 53–64.
13.
SandorG. N.Principles of a general quaternion-operator method of spatial kinematic synthesis. Trans. ASME J. Appl. Mechanics, 1968, 90(1), 40–46.
14.
AroraJ. S.Introduction to optimum design, 1989, pp. 330–336 (McGraw-Hill, New York).
15.
VanderplaatsG. N.User's manual for ADS, Version 2.01, 1987 (Engineering Design Optimization Inc.).
