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.

翻译：设计机械连杆以实现目标末端执行器轨迹是一个基础性挑战，这源于连续节点布局、离散拓扑构型与非线性运动学约束之间复杂的耦合关系。高度非线性的运动-构型映射意味着关节位置的微小扰动会显著改变轨迹，而组合爆炸的设计空间使得传统优化与启发式方法在计算上难以处理。我们提出了一种自回归扩散框架，该框架利用连杆组装的二元特性，将机构表示为顺序构建的图结构，其中节点对应关节，边对应刚性连杆。我们的方法结合了因果Transformer与去噪扩散概率模型（DDPM），两者均以通过Transformer编码器编码的目标轨迹为条件。因果Transformer以自回归方式逐节点预测离散拓扑，而DDPM则细化每个节点的空间坐标及其与已生成节点间的边连接关系。这种顺序生成机制支持自适应试错式综合，能够针对出现运动学锁死或碰撞的问题节点进行选择性重新生成，从而在设计过程中自主修正退化构型。我们基于图的数据驱动方法超越了传统优化途径，实现了可扩展的逆向设计，并能泛化至具有任意节点数量的机构。我们成功合成了包含多达20个节点的连杆系统，并展示了其向N节点架构的可扩展性。此项工作推进了自回归图生成方法与计算运动学综合领域的发展，为复杂机械系统的可扩展逆向设计建立了新范式。