Synthesis of Four-Link Initial Kinematic Chains with Spherical Pairs for Spatial Mechanisms

• DOI: 10.20944/preprints202502.1022.v1
• Publication Date: 2025-02-17T00:43:36Z
• Authors: Algazy Zhauyt; Kuanysh Alipbayev; Serikbay Kosbolov; Alisher Aden; Aray Orazaliyeva; Samal Abdreshova
• Keywords: Link (geometry)

This research addresses the problem of initial synthesis kinematic chains with spherical pairs, which are essential in design spatial mechanisms used robotics, aerospace, and mechanical systems. The goal is to establish existence solutions for defining geometric motion constraints these chains, ensuring that synthesized mechanism achieves desired precision. By formulating terms nonlinear algebraic equations derived from positions orientations links, we analyze conditions under a valid solution exists. We explore both analytical numerical methods solve equations, highlighting significance parameter selection determining feasible solutions. study further investigates impact parameters on stability flexibility chain. findings provide theoretical foundation guiding practical joints, accuracy reliability complex tasks. work presents comprehensive framework 3D visualization transformations coordinate relationships using Python 3.13.0. Leveraging capabilities libraries such as NumPy Matplotlib, develop series modular code examples illustrate how plot multidimensional data pertinent chain robotic mechanisms. Specifically, our approach demonstrates fixed points, XA, YA, ZA, xB, yB, zB, xC, yC, zC, alongside their differences respect reference points transformation matrices. detail plotting components, including rotation matrix elements (e, m, n) products matrices, well representation angular (θi, ψi, i) three-dimensional context. proposed techniques not only facilitate debugging analysis behaviors but also flexible tool researchers computer graphics, design. offering clear interactive strategy, this enhances understanding dynamics inherent multi-body