The Mechanism for Force Measurement and Guidance Based on Reciprocal Measurement in Joule Balance

The Joule balance is a kilogram realization method based on Planck’s constant. In Joule balance, alignment error is the main uncertainty component. In order to solve the problem, the dual-mode reciprocal measurement method of Joule balance is analyzed in this article. We establish the reciprocal relationship between the parasitic generalized force in the weighing phase and the parasitic displacement in flux difference measurement mode. In addition, it is concluded that the integrated mechanism with force measurement and guidance is the base of reciprocal measurement. Then, an integrated mechanism of force measurement and guidance is designed with three parallelogram flexible hinges. The small axial stiffness and large off-axial stiffness are achieved to ensure force measurement and guidance. Theoretical and finite element analysis are applied to the mechanism. Experiment setups are built for force-measurement sensitivity and straightness. The force-measurement sensitivity of the mechanism is 7.2 mN/mm; within the guiding displacement of 17.2 mm, the straightness is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$4.32~\mu $ </tex-math></inline-formula>m. The integrated mechanism can be used for force measurement and guidance simultaneously. In conclusion, the dual-mode reciprocal measurement can be achieved in Joule balance.