LinkD: AutoRegressive Diffusion Model for Mechanical Linkage Synthesis

TL;DR

This paper introduces LinkD, an autoregressive diffusion model that enables scalable, data-driven inverse design of complex mechanical linkages with arbitrary node counts, surpassing traditional optimization methods.

Contribution

The paper presents a novel autoregressive diffusion framework combining a causal transformer and DDPM for sequential, adaptive linkage synthesis, handling complex nonlinear kinematic constraints.

Findings

Successfully synthesizes linkages with up to 20 nodes

Outperforms traditional optimization in scalability and flexibility

Enables autonomous correction of degenerate configurations

Abstract

Designing mechanical linkages to achieve target end-effector trajectories presents a fundamental challenge due to the intricate coupling between continuous node placements, discrete topological configurations, and nonlinear kinematic constraints. The highly nonlinear motion-to-configuration relationship means small perturbations in joint positions drastically alter trajectories, while the combinatorially expanding design space renders conventional optimization and heuristic methods computationally intractable. We introduce an autoregressive diffusion framework that exploits the dyadic nature of linkage assembly by representing mechanisms as sequentially constructed graphs, where nodes correspond to joints and edges to rigid links. Our approach combines a causal transformer with a Denoising Diffusion Probabilistic Model (DDPM), both conditioned on target trajectories encoded via a transformer encoder. The causal transformer autoregressively predicts discrete topology node-by-node, while the DDPM refines each node's spatial coordinates and edge connectivity to previously generated nodes. This sequential generation enables adaptive trial-and-error synthesis where problematic nodes exhibiting kinematic locking or collisions can be selectively regenerated, allowing autonomous correction of degenerate configurations during design. Our graph-based, data-driven methodology surpasses traditional optimization approaches, enabling scalable inverse design that generalizes to mechanisms with arbitrary node counts. We demonstrate successful synthesis of linkage systems containing up to 20 nodes with extensibility to N-node architectures. This work advances autoregressive graph generation methodologies and computational kinematic synthesis, establishing new paradigms for scalable inverse design of complex mechanical systems.