🤖 AI Summary
This work addresses the one-to-many mapping challenge in planar path synthesis—where a single target trajectory corresponds to multiple linkage mechanisms (e.g., four-bar, six-bar, eight-bar)—by proposing a unified framework based on conditional autoregressive sequence generation. The approach formulates mechanism synthesis as a discrete sequence generation task, leveraging a decoder-only Transformer integrated with a variational autoencoder (VAE). By quantizing joint coordinate sequences, incorporating explicit mechanism-type tokens, and employing bounded latent-space noise scheduling, the model enables retrieval-free generation of diverse, high-fidelity designs. A novel ordered structure-aware Gaussian smoothing auxiliary loss is introduced to enhance geometric coherence, while dynamic time warping (DTW), Chamfer distance, and forward kinematics are jointly utilized for geometric alignment and evaluation. Experiments demonstrate strong performance on held-out test sets, achieving average Chamfer distance of 0.0132 and DTW of 0.153; further gains are realized via a VAE latent-space k-nearest-neighbor topology matching baseline, yielding Chamfer distance of 0.0071 and DTW of 0.117.
📝 Abstract
Planar path synthesis requires mechanisms whose coupler curves match a prescribed trajectory; the mapping from curve to linkage is inherently one-to-many across four-, six-, and eight-bar topologies. We address this design problem with simulation-grounded evaluation on a curated corpus of over one million mechanisms, reporting Chamfer distance and dynamic time warping after forward kinematics and geometric alignment. We formulate synthesis as conditional autoregressive sequence modeling: joint coordinates are uniformly quantized to tokens and generated by a decoder-only transformer with a variational-autoencoder (VAE) latent of the target curve and an explicit mechanism-type token. Training combines token cross-entropy with a Gaussian-smoothed bin auxiliary loss that respects ordinal structure among bins. At inference, a bounded latent-noise schedule decodes all mechanism types at each noise level; we retain the top five candidates by geometric error, yielding diverse accurate families without dataset lookup. On held-out tests, aggregate mean Chamfer distance is $0.0132$ and mean dynamic time warping is $0.153$; a latent $k$-nearest-neighbor baseline that conditions on training-set neighbor latents in VAE space achieves matched-topology mean Chamfer distance $0.0071$ and mean dynamic time warping $0.117$ using the same decoder.