Co-design Optimization of Moving Parts for Compliance and Collision Avoidance

TL;DR

This work addresses co-design of moving mechanical parts under physics-based stiffness and collision avoidance by coupling topology optimization loops with a differentiable collision measure. A precomputed collision weight matrix derived from relative motions enables scalable, gradient-based optimization that combines a topological sensitivity field with collision gradients in a Pareto-tracing framework. The method is validated across 2D and 3D examples (cam-follower, three-square assemblies, gripper-cams, and a 3D three-body system), producing collision-free, high-stiffness designs with practical computation times. The approach extends topology optimization from single-part design to assembly-level co-design, enabling complex, collision-free shapes tailored to prescribed motions and performance constraints.

Abstract

Design requirements for moving parts in mechanical assemblies are typically specified in terms of interactions with other parts. Some are purely kinematic (e.g., pairwise collision avoidance) while others depend on physics and material properties (e.g., deformation under loads). Kinematic design methods and physics-based shape/topology optimization (SO/TO) deal separately with these requirements. They rarely talk to each other as the former uses set algebra and group theory while the latter requires discretizing and solving differential equations. Hence, optimizing a moving part based on physics typically relies on either neglecting or pruning kinematic constraints in advance, e.g., by restricting the design domain to a collision-free space using an unsweep operation. In this paper, we show that TO can be used to co-design two or more parts in relative motion to simultaneously satisfy physics-based criteria and collision avoidance. We restrict our attention to maximizing linear-elastic stiffness while penalizing collision measures aggregated in time. We couple the TO loops for two parts in relative motion so that the evolution of each part's shape is accounted for when penalizing collision for the other part. The collision measures are computed by a correlation functional that can be discretized by left- and right-multiplying the shape design variables by a pre-computed matrix that depends solely on the motion. This decoupling is key to making the computations scalable for TO iterations. We demonstrate the effectiveness of the approach with 2D and 3D examples.

Figures (27)

• Figure 1: Motion of the Gripper and two cams.
• Figure 2: Pair-wise collision fields for the gripper and the two cams.
• Figure 3: Overall collision fields over the Gripper and two cams. Since the two cams only collides with the gripper, their overall collision field is similar to the their pair-wise collision fields with the gripper.
• Figure 4: Collision gradient fields over the Gripper and two cams.
• Figure 5: Computing the topological sensitivity by hypothetically perturbing the design $\Omega$ at point ${\mathbf{x}}$ via a small inclusion of radius $\epsilon$.