7.1 Introduction

In a highly mechanized world, force and torque are among the most important of all measured quantities [1 4]. They play a significant role in products from weighing machines and load cells used in industrial and retailing applications, to automotive and aerospace engines, screw caps on medicine bottles, and nut and bolt fasteners. Forces and torques can range from greater than 10 kN to less than 1 ?N, and from 50 kNm to below 1 Nm, respectively. Measurement accuracy levels required can vary widely from, say, 5% to better than 0.01% of full scale ranges, depending on the application. Hysteresis and nonlinear effects in the mechanical structures of measuring devices need to be small, and measurement resolutions need to be high. Measurement devices need to be robust to withstand changing environmental influences such as temperature, vibration, and humidity, and they must also provide reliable measurement over long periods of time. Mechanical interfacing of the devices can be difficult and can influence final measurement. The forces and torques may change rapidly, and so the devices must have adequate frequency and transient responses.

There are several methods to measure forces and torques. Often, the force to be measured is converted into a change in length of a spring element. The change in dimensions is subsequently measured by a sensor, for example, a piezoresistive, a capacitive or a resonant sensor.

It is not so surprising, therefore, that most force and torque measurement devices...