Practical considerations of joint friction and backlash in large ground-based telescope secondary optic positioning systems

Abstract

Secondary mirrors and lenses in several planned ground-based telescopes have masses on the order of 5000 kg and require a positioning system that is repeatable to one-tenth the pixel size of the optical sensors, nominally 10 micrometers or less. Hexapods, or Stewart Platforms, are frequently integrated into the support structure as six degree of freedom parallel positioning and alignment systems. These systems are limited in resolution by friction in the 36 kinematic degrees of freedom (DOF) necessary for properly constrained motion of the platform. The 30 passive DOF, typically implemented with one 3-DOF and one 2-DOF joint on each hexapod leg, introduce unwanted friction and/or backlash into the positioning system. Backlash is generally unacceptable and elimination requires significant preloading of the joints, which in turn increases joint friction. This paper will: review various joint types including rolling element, plain bearing (sliding), and flexure; examine the backlash and friction tradeoffs involved in selecting joint type including unwanted deflections due to joint moments, static position resolution limitations, dynamic positioning settling time effects, self-locking mechanisms, and power dissipation; compare with experimental data and previously published results; present methods for modeling both static and dynamic effects of friction; and suggest recommendations for general positioning system design. Considerations for both equatorial and altitude-azimuth telescopes will be discussed, along with variation of effects due to telescope positioning. Analyses will be reinforced with friction and backlash measurements made on several physical joints.