Unveiling the Complete Variant of Spherical Robots

TL;DR

This paper systematically enumerates all possible variants of spherical ($SO(3)$) parallel robots using an analytical velocity-level approach, enabling comprehensive exploration of their architectures and potential applications.

Contribution

It introduces a generalized analytical method to identify all 73 limb types and over 5300 variants of spherical robots, expanding beyond case-by-case analysis.

Findings

Identified 73 non-redundant limb types for $SO(3)$ motion.

Explored 5329 spherical robot variants with diverse capabilities.

Provided a systematic framework for designing novel spherical robots.

Abstract

This study presents a systematic enumeration of spherical ($SO(3)$) type parallel robots' variants using an analytical velocity-level approach. These robots are known for their ability to perform arbitrary rotations around a fixed point, making them suitable for numerous applications. Despite their architectural diversity, existing research has predominantly approached them on a case-by-case basis. This approach hinders the exploration of all possible variants, thereby limiting the benefits derived from architectural diversity. By employing a generalized analytical approach through the reciprocal screw method, we systematically explore all the kinematic conditions for limbs yielding $SO(3)$ motion.Consequently, all 73 possible types of non-redundant limbs suitable for generating the target $SO(3)$ motion are identified. The approach involves performing an in-depth algebraic motion-constraint analysis and identifying common characteristics among different variants. This leads us to systematically explore all 73 symmetric and 5256 asymmetric variants, which in turn become a total of 5329, each potentially having different workspace capability, stiffness performance, and dynamics. Hence, having all these variants can facilitate the innovation of novel spherical robots and help us easily find the best and optimal ones for our specific applications.