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

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.

Nonlinear Analysis of a Class of Inversion-Based Compliant Cross-Spring Pivots

This paper presents a nonlinear model of an inversion-based generalized cross-spring pivot (IG-CSP) using the beam constraint model (BCM), which can be employed for the geometric error analysis and the characteristic analysis of an inversion-based symmetric cross-spring pivot (IS-CSP). The load-dependent effects are classified in two ways, including the structure load-dependent effects and beam load-dependent effects, where the loading positions, geometric parameters of elastic flexures, and axial forces are the main contributing factors. The closed-form load-rotation relations of an IS-CSP and a non-inversion-based symmetric cross-spring pivot (NIS-CSP) are derived with consideration of the three contributing factors for analyzing the load-dependent effects. The load-dependent effects of IS-CSP and NIS-CSP are compared when the loading position is fixed. The rotational stiffness of the IS-CSP or NIS-CSP can be designed to increase, decrease, or remain constant with axial forces, by regulating the balance between the loading positions and the geometric parameters. The closed-form solution of the center shift of an IS-CSP is derived. The effects of axial forces on the IS-CSP center shift are analyzed and compared with those of a NIS-CSP. Finally, based on the nonlinear analysis results of IS-CSP and NIS-CSP, two new compound symmetric cross-spring pivots are presented and analyzed via analytical and FEA models.

Nonlinear Analysis of a Class of Inversion-Based Compliant Cross-Spring Pivots

This paper presents a nonlinear model of an inversion-based generalized cross-spring pivot (IG-CSP) using the beam constraint model (BCM), which can be employed for the geometric error analysis and the characteristic analysis of an inversion-based symmetric cross-spring pivot (IS-CSP). The load-dependent effects are classified in two ways, including structure load-dependent effects and beam load-dependent effects, where the loading positions, geometric parameters of elastic flexures, and axial forces are the main contributing factors. The closed-form load-rotation relations of an IS-CSP and a non-inversion-based symmetric cross-spring pivot (NIS-CSP) are derived with consideration of the three contributing factors for analyzing the load-dependent effects. The load-dependent effects of IS-CSP and NIS-CSP are compared when the loading position is fixed. The rotational stiffness of the IS-CSP or NIS-CSP can be designed to increase, decrease, or remain constant with axial forces, by regulating the balance between the loading positions and the geometric parameters. The closed-form solution of the center shift of an IS-CSP is derived. The effects of axial forces on the IS-CSP center shift are analyzed and compared with those of a NIS-CSP. Finally, based on the nonlinear analysis results of IS-CSP and NIS-CSP, two new compound symmetric cross-spring pivots are presented and analyzed via analytical and FEA models.

Effects of composition and pressure on electronic states of iron in bridgmanite

Electronic states of iron in the lower mantle's dominant mineral, (Mg,Fe,Al)(Fe,Al,Si)O3 bridgmanite, control physical properties of the mantle including density, elasticity, and electrical and thermal conductivity. However, the determination of electronic states of iron has been controversial, in part due to different interpretations of Mössbauer spectroscopy results used to identify spin state, valence state, and site occupancy of iron. We applied energy-domain Mössbauer spectroscopy to a set of four bridgmanite samples spanning a wide range of compositions: 10–50% Fe/total cations, 0–25% Al/total cations, 12–100% Fe3+/total Fe. Measurements performed in the diamond-anvil cell at pressures up to 76 GPa below and above the high to low spin transition in Fe3+ provide a Mössbauer reference library for bridgmanite and demonstrate the effects of pressure and composition on electronic states of iron. Results indicate that although the spin transition in Fe3+ in the bridgmanite B-site occurs as predicted, it does not strongly affect the observed quadrupole splitting of 1.4 mm/s, and only decreases center shift for this site to 0 mm/s at ~70 GPa. Thus center shift can easily distinguish Fe3+ from Fe2+ at high pressure, which exhibits two distinct Mössbauer sites with center shift ~1 mm/s and quadrupole splitting 2.4–3.1 and 3.9 mm/s at ~70 GPa. Correct quantification of Fe3+/total Fe in bridgmanite is required to constrain the effects of composition and redox states in experimental measurements of seismic properties of bridgmanite. In Fe-rich, mixed-valence bridgmanite at deep-mantle-relevant pressures, up to ~20% of the Fe may be a Fe2.5+ charge transfer component, which should enhance electrical and thermal conductivity in Fe-rich heterogeneities at the base of Earth's mantle.