Modeling and validation of vertical direction force estimation with a three-dimensional force measurement instrument based on a zero-compliance mechanism

The principle of a zero-compliance mechanism was used to develop a three-dimensional force measurement instrument. In each axis, the point of force is suspended by a zero-compliance mechanism. A vertical axis force estimation operation imitates the structure of a double series magnetic suspension system. An electromagnet directly controls the movement of the first suspended object (floator), which is denoted as a detection point, and indirectly controls the motion of the second floator, which is denoted as a point of force. Indirect control of the point of force is executed by the attractive force of a permanent magnet that is fixed to the bottom part of the detection point. To achieve zero-compliance, a Proportional-Integral-Derivative (PID) control is applied to the point of force, and to make the system stable, a Proportional-Derivative (PD) control is also applied to the detection point. In such suspension conditions, when force is exerted on the point of force, the displacement of the second floator is regulated to maintain its primary position while the detection point displaces in proportion to the applied force. Thus, a zero-compliance condition is maintained at the point of force, and the external force is measured from the linear displacement of the detection point. To restrict the motions of the detection point and the point of force in translation only, they are supported with leaf springs. This paper presents the modeling of the vertical direction force measurement operation of the developed three-axis force estimation instrument, and the theoretical analyses were validated by experiments of force measurement in both the millinewton and micronewton ranges.