Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis

Daniel Huczala; Severinas Zube; Martin Pfurner; Johannes Siegele; Frank C. Park

cs.ROFeb 24, 2026

Computer-Aided Design of Rational Motions for 4R and 6R Spatial Mechanism Synthesis

Authors: Daniel Huczala, Severinas Zube, Martin Pfurner, Johannes Siegele, Frank C. Park

Organizations: Robotics Laboratory, Seoul National University, Seoul, Korea · Institute of Computer Science, Department of Mathematics and Informatics, Vilnius University, Vilnius, Lithuania · Unit of Geometry and Surveying, University of Innsbruck, Innsbruck, Austria · J. Radon Instit. for Computational and Applied Mathematics (RICAM), Austrian Academy of Sciences, Linz, Austria

Abstract

This paper focuses on geometric methods for generating rational motions used in the design of single-loop rational linkages, 1-degree-of-freedom mechanisms that can execute prescribed spatial tasks. Building on established rational motion synthesis methods, we introduce a new interpolation scheme for seven 3D points based on cubic quaternionic Bezier curves. The resulting motion admits factorization, i.e. the synthesis of a spatial six-bar mechanism whose tool frame passes the specified seven points. To support engineering practice, we provide open-source CAD tools that implement also the other methods and provide fast visual evaluation of motion generation and mechanism synthesis.

Figures & tables

Panel of Figure 1 — Figure 1: Left: Motion Designer – an interactive plot of a 1-DoF motion that interpolates 7 given points (purple); right: example of a produced 6R prototype.

Mechanism Design

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Jun 16, 2026J/K move · Enter open · S save

Discrete Autoregressive Transformer for Generative Mechanism Synthesis

Anar Nurizada, Anurag Purwar

Computer-Aided Design and Innovation Lab, Department of Mechanical Engineering, Stony Brook University, Stony Brook, NY 11794-2300, USA

Autoregressive Generation Conditional Generative Modeling

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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.

Abstract

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