Triple Crossed Flexure Pivot Based on a Zero Parasitic Center Shift Kinematic Design

Abstract

Thanks to their absence of play, absence of contact friction and possible monolithic fabrication, flexure pivots offer advantages over traditional bearings in small-scale, high accuracy applications and environments where lubrication and wear debris are proscribed. However, they typically present a parasitic center shift that deteriorates their rotational guidance accuracy. Existing solutions addressing this issue have the drawbacks of reducing angular stroke, prohibiting planar design, or introducing overconstraints or underconstraints. This article introduces a new triple crossed flexure pivot called TRIVOT that has a reduced parasitic center shift without overconstraints nor internal mobility, while allowing either optimal stress distribution in the flexures or a planar design. The new architecture also makes it possible to place the center of rotation outside of the physical structure, which is not the case with traditional bearings. Based on finite element simulations, we show that the parasitic shift is reduced by one order of magnitude in comparison to the widely used crossed flexure pivot. We also derive and validate formulas for the rotational stiffness and angular stroke limit of the TRIVOT. Finally, we show that a high support stiffness can be achieved with a lowest uwanted eignenfrequency 13.5 times higher than the first eigenfrequency. We expect this new pivot to become a competitive alternative to the crossed flexure pivot for applications where high accuracy and compactness are required.

Gravity-Compensation Design Approaches for Flexure-Pivot Time Bases

“…The evaluation of these approaches in terms of chronometric accuracy on designs and prototypes satisfying realistic mechanical watch specifications. This is demonstrated on two flexure-pivot oscillator architectures developed in previous research: the co-RCC [4,6,8] (Figure 1a) and the TRIVOT [10,21] (Figure 1b). For the co-RCC oscillator, watch-scale silicon prototypes are used to validate experimentally the presented approaches.…”

“…The main known cause for in-plane gravity effects on the stiffness of flexure pivots is their parasitic center shift. It is well-known that flexure pivots only approximate a rotational motion [10,15,16,[22][23][24][25] and, in the case of a flexure-pivot oscillator, their center shift displaces the center of mass (COM) of the inertial body. The action of gravity on this displaced COM results in a torque that either contributes to the restoring torque of the flexures (positive stiffness contribution) or drives the oscillator away from its equilibrium (negative stiffness contribution).…”

“…An even greater center shift reduction is accomplished in the design of the TRIVOT oscillator (Figure 1b). Indeed, it is based on a theoretical kinematic design that theoretically has zero parasitic shift [10]. In practice, each main flexure is connected in series to parallel flexures having a radial DOF that absorbs the radial shortening of the main flexures as the pivot rotates.…”

“…In practice, each main flexure is connected in series to parallel flexures having a radial DOF that absorbs the radial shortening of the main flexures as the pivot rotates. This has the consequence of reducing the center shift by one order of magnitude in comparison to the standard cross-spring pivot [10]. In order to provide realistic timekeeping accuracy data, a monolithic silicon TRIVOT oscillator satisfying mechanical watch specifications was designed.…”

“…Flexure time bases have gained significant traction in the watchmaking industry in the past decade thanks to their high quality factor and monolithic design offering the prospect of increased timekeeping accuracy, increased power reserve, reduced maintenance and simplified assembly [1][2][3][4]. They have been the topic of our previous research [4][5][6][7][8][9][10], and recently gave rise to commercial products [11][12][13]. These mechanisms use the deformation of slender elastic elements, i.e., flexures, to guide their motion [14][15][16].…”