Numerical analysis of large deflection of the cantilever beam subjected to a force pointing at a fixed point

Abstract

In many cable-driven compliant mechanisms, the need for controlled motion in the flexible structure often demands the actuation cables to pass through a fixed point (e.g. a cable routing channel in a segment disk or a fixed pulley) to constrain the force angle on the cable. This condition can be modeled as the large deflection problem of a cantilever beam with two parameters, namely the distal slope and the force angle, which is more complex than the regular one-parameter deflection problem of cantilever beams. In order to solve this mechanics problem, a numerical method based on variable transformation and heuristic cuckoo search (CS) algorithm is presented to analyze the large deflection shape of a beam subjected to a tip force pointing at a fixed point. Firstly, a two-parameter second-order differential equation governing the cantilever beam with large deflection and tip force constrained to a particular point is established. Secondly, a new variable is defined to replace the two parameters based on the variable transformation, allowing the governing equation to be simplified to a one-parameter second-order differential equation. Thirdly, this mathematical problem is written as a one-parameter optimization problem that can be solved by the CS algorithm. The proposed approach is then verified by commercial finite element analysis solution. Comprehensive simulation results and analysis are presented under different combinations of critical parameters, leading to potentially more accurate model-based design for compliant structures under the studied force constraint.