On Determining Parameters of the Twist-Axis for the Finite Displacement of a Body

1991 ◽  
pp. 71-80
Author(s):  
I. A. Parkin
Keyword(s):  
Finite Displacement

An Investigation of Screw Systems in the Finite Displacements of Bennett-Based 6R Linkages

1999 ◽  
Vol 122 (4) ◽  
pp. 426-430 ◽  
Author(s):  
Chintien Huang ◽  
Chi-Chih Sun
Keyword(s):  
Numerical Simulations ◽  
Second Order ◽  
Finite Displacement ◽  
Finite Displacements ◽  
Overconstrained Linkages

This paper investigates, via numerical simulations, the finite displacements of all the known Bennett-based 6R overconstrained linkages: Goldberg’s 6R, variant Goldberg 6R, Waldron’s hybrid 6R, and Wohlhart’s hybrid 6R linkages. An investigation of the finite displacements of nine distinct linkages reveals that every Bennett-based 6R linkage, except for the isomerization of Wohlhart’s hybrid linkage, inherits the linear properties of the Bennett mechanism. The relative finite displacement screws of some non-adjacent links of these linkages form screw systems of the second order. Thirty-one screw systems are reported in this paper. [S1050-0472(00)02204-2]

Effect of the coordinate frame on high-order expansion of serial-chain displacement

2019 ◽  
Vol 233 (4) ◽  
pp. 840-855
Author(s):  
Paul Milenkovic
Keyword(s):  
Common Ground ◽  
Power Series Expansion ◽  
Hardware Acceleration ◽  
Asymptotic Limit ◽  
Terminal Link ◽  
Coordinate Frame ◽  
Alternative Formulation ◽  
Moving Frames ◽  
Finite Displacement ◽  
Instantaneous Screw

An algorithmic differentiation technique gives a simpler, faster power series expansion of the finite displacement of a closed-loop linkage. It accomplishes this by using a higher order than what has been implemented by complicated prior formulas for kinematic derivatives. In this expansion, the joint rates and axis lines generate the instantaneous screw of each link. Constraining the terminal link to have a zero instantaneous screw satisfies closure. In order to maintain closure over a finite displacement, it is necessary to track the spatial trajectory of each joint axis line, which in turn is directed by the instantaneous screw of a link to which it is attached. Prior algorithms express these screws in a common ground-referenced coordinate frame. Motivated by the kinematics solver portion of the recursive Newton–Euler algorithm, an alternative formulation uses sparse matrices to update the instantaneous screw between successive link-local frames. The recursive Newton–Euler algorithm, however, conducts the expansion to only second order, where this paper shows local coordinate frames that are only instantaneously aligned with their respective links give identical expressions to those in frames that move with the links. Moving frames, however, require about 40% of the operations of the global-frame formulation in the asymptotic limit. Both incrementally translated (Java) and statically compiled (C++) software implementations offer more modest performance gains; execution profiling shows reasons in order of importance (1) balance of calculation tasks when below the asymptotic limit, (2) Java array bounds checking, and (3) hardware acceleration of loops.

scholarly journals An elastic finite displacement analysis of plane beams with and without shear deformation.

1986 ◽  
pp. 169-177 ◽  
Author(s):  
Taweep CHAISOMPHOB ◽  
Fumio NISHINO ◽  
Akio HASEGAWA ◽  
Abdel-Shafy ALYGAMALALY
Keyword(s):  
Shear Deformation ◽  
Displacement Analysis ◽  
Finite Displacement

scholarly journals A Finite Displacement Formulation of Elastic Shells (By Takamasa SAKURAI, Akio HASEGAWA and Fumio NISHINO)

1983 ◽  
Vol 1983 (340) ◽  
pp. 213-214
Author(s):  
Masaharu Hirashima ◽  
Teruhiko Yoda ◽  
Masashi Iura ◽  
Takamasa SAKURAI ◽  
Akio HASEGAWA ◽  
...  
Keyword(s):  
Elastic Shells ◽  
Finite Displacement
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