Generation of Link Mechanism by Shape-Topology Optimization of Trusses Considering Geometrical Nonlinearity

Abstract

A two-stage general optimization approach is presented for generating link mechanisms from a highly connected ground structure. The structure is modeled as a pinjointed truss, which is to be optimized so that a large displacement is generated in the specified direction at the output node. The design variables are the cross-sectional areas of the members and the nodal locations. The equilibrium path of an unstable mechanism is traced by the displacement control method. In the first step, the unnecessary members are removed by solving the optimization problem for minimizing the total structural volume under constraints on the maximum load, the displacement at the specified node, and the stiffnesses at the initial and final states. In the second step, the deviation of the displacement of the output node from the specified direction is minimized. It is shown in the numerical examples that several mechanisms can be naturally found as a result of the two-stage optimization starting from randomly selected initial solutions.

Topology optimization of planar linkage systems involving general joint types

“…(20) and Eq. (21), η denotes the mean value of the work transmittance efficiency functions η t ⁎ at time t ⁎ .…”

“…The function ψ t ⁎(ξ) denotes a Euclidean distance error between the current center position r Q,t ⁎(ξ) of the end-effector Q and the target position rQ ;t à at analysis step t ⁎ . When the distance error becomes smaller than a given error bound ε at every analysis step, the current output path becomes nearly the same as the target path and a desired linkage mechanism is synthesized as the result of (20). Eq.…”

“…The external force F ext,t is a force intentionally applied to the system against the motion of the end-effector Q. It is crucial to apply F ext ,t in order to make formulation (20) meaningful. The specific form of F ext,t will be given later and we will now focus on how the input energy is converted inside the D-SBM system.…”

“…Solving (20) requires an optimization algorithm. As a gradient optimizer, the method of moving asymptotes [37] is used.…”

“…An attempt for the simultaneous synthesis using a genetic algorithm was reported [12] but the synthesis of an arbitrary topology with dimensional synthesis was not performed. Thus, topology optimizations of linkage systems, which simultaneously determine the number and dimension of a desired linkage mechanism, have been previously studied [13][14][15][16][17][18][19][20][21][22][23][24][25]. Among them, gradient-based methodologies [13,15,16,[18][19][20]22,24,25] are promising because of their computational efficiency.…”