With the current drive towards diffraction limited storage rings, hard x-ray optics will require subsequent increases in positioning accuracy over large travel ranges. Nanometer-level precision positioning requires the use of compliant mechanisms to remove friction and backlash type errors. Ideally, the compliant mechanism is compliant in the direction of desired travel and rigid in all other directions. However, in reality, there is still compliance in these other directions, particularly for flexure pivots, which lead to parasitic trajectory errors. In this paper we analyze the trajectory errors of a linear guiding mechanism, composed of commercially available C-Flex Bearing Co. Inc. and Riverhawk Co. flexure pivots, using finite element analysis and experimental measurements. The guide is designed as an assembly of double parallel 4-bar type deformation compensated linear guiding mechanisms, and incorporates a novel 1:2 stabilizer unit to control the middle-bar. The focus of the analysis is on the trajectory errors caused by rotation center shift, manufacturing tolerances, flexure pivot size, assembly tolerances, and includes a discussion of methods to mitigate these errors.
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