Synthesis of 1-DOF hinging rigid panel structure kinematic transmissions using evolutionary algorithms

Abstract

Origami structures are found in mechanical technology more and more often. A less strict derivative of origami are Hinging Rigid Panel Structures, which are not bound to be developable from a single flat sheet of planar material. These Hinging Rigid Panel Structures can be applied to many fields of mechanical design, and moreover are interesting for their kinematic behaviour. The benefits of using a structure that originates from pieces of flat material include but are not limited to being able to surface treat uninterrupted sections of material that can subsequently be folded into part of the structure’s configuration. In order to describe and programmatically manipulate Hinging Rigid Panel Structures and their kinematics adequately and systematically, this research takes a new and specific approach on modelling them. The Hinging Rigid Panel Structures are modelled as 1-DOF mechanisms, consisting of a base pyramid, to which 2 arms of a variable amount of pairs of triangles are attached. To sufficiently test the versatility of this method of describing Hinging Rigid Panel Structures, a classification has been set up to cover a range of kinematic input-output relations, which will be used to test algorithms against. This classification differentiates by dimension and displacement distribution over both the input and output curves, and captures all kinematic transmissions in 1545 cases. With a sample size of np = 10 randomly generated versions of each of these input-output relations and a motion path resolution of rc = 25, a data set was generated using this classification method. An evolutionary algorithm was created to navigate the solution space more efficiently than using conventional algorithms like (gradient based) hill climber algorithms. The main variables of the evolutionary algorithm like generation size (sg = 60), amount of generations (ng = 75), mutation rate amount (nm = 180) and parent splicing methods have empirically been determined. Running the optimisation for all the categories of the previously mentioned classification was done by adapting the code to be able to be run in crowd computational capacity across 17 contributors’ computers. The results show that Hinging Rigid Panel Structure mechanisms are to a certain extend able to be synthesised to generate requested transmissions, but some cases are harder to reach than others. Complex compound 3D paths are harder to optimise for than other categories, such as planar circular motions. This research lays out a valuable basis that contains all aspects to create a reasonable performing optimiser for 3-D Hinging Rigid Panel Structures that follow requested input-output relations. This research could for example be used as a starting point for developing a software package that allows designers to implement Hinging Rigid Panel Structures in their CAD designs for mechanical transmissions.