Theoretical Characteristics of a three-point Roberts Linkage

TL;DR

This paper explores the theoretical properties of a three-point Roberts linkage, focusing on its potential for vibration isolation in gravitational wave detectors, by deriving key parameters and analyzing error responses.

Contribution

It introduces a theoretical framework for a three-point Roberts linkage as a vibration isolation system, including equations for key parameters and error analysis.

Findings

Derived equations for equivalent pendulum length and motion relationships.

Analyzed the linkage's behavior under various error conditions.

Demonstrated potential application in gravitational wave antenna development.

Abstract

The Roberts linkage is recognized for enabling long-period pendulum motion in a compact format. Utilizing this characteristic, we are developing a three-point Roberts linkage for vibration isolation systems, with an eye towards its potential contribution to the development of next-generation interferometric gravitational wave antennas. In this article, we derived the equations to determine the essential parameters when using this linkage as a vibration isolation system, namely the equivalent pendulum length and the relationship between translational motion of the center of mass and rigid body rotation, from size parameters. Additionally, we analyzed the behavior in response to various errors.