Morphing of and writing with a scissor linkage mechanism

TL;DR

This paper investigates the kinematics of scissor-linkage mechanisms, deriving their motion properties, and demonstrates their potential for shape morphing and writing tasks through optimization and experimental validation.

Contribution

It introduces a geometric and optimization framework for programming shape-changing tasks in scissor-linkage mechanisms, enabling automated navigation and inspection applications.

Findings

Effective curvature and tip trajectory expressions derived

Optimization-based programming successfully implemented in experiments

Challenges remain in rapid programming and error-free execution

Abstract

Kinematics of mechanisms is intricately coupled to their geometry and their utility often arises out of the ability to perform reproducible motion with fewer actuating degrees of freedom. In this article, we explore the assembly of scissor-units, each made of two rigid linear members connected by a pin joint. The assembly has a single degree of freedom, where actuating any single unit results in a shape change of the entire assembly. We derive expressions for the effective curvature of the unit and the trajectory of the mechanism's tip as a function of the geometric variables which we then use as the basis to program two tasks in the mechanism: shape morphing and writing. By phrasing these tasks as optimization problems and utilizing the differentiable simulation framework, we arrive at solutions that are then tested in table-top experiments. Our results show that the geometry of scissor assemblies can be leveraged for automated navigation and inspection in complex domains, in light of the optimization framework. However, we highlight that the challenges associated with rapid programming and error-free implementation in experiments without feedback still remain.