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

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.

The Application of Pushover Method in Complex Bridge Seismic Design

Elasto-plastic seismic response analysis of complex bridge requires large computation, thus in practical engineering design this method can be simplified according to finite energy principle, finite displacement principle and Pushover method or other approximation algorithms. Finite energy principle and finite displacement principle are applied to piers with simple damage mode, and the two principles differ in structure’s natural mode of vibration. Pushover applied to complex structures which can’t be analyzed as single pier. Pushover gives maximum seismic response by static nonlinear analysis, and current Japanese specification adopts Pushover for complex bridge seismic design such as continuous rigid bridges.