Force Transducers
Force transducers are required to transform a physical force into an electrical signal. Their uses in the Robotics field have traditionally been confined to specialized, custom-built applications and therefore are limited in number. The advent and development of adaptive control techniques, however, have increased the popularity of force and torque sensors which will allow the next generation of robots to interactively control the gripping action as well as the object movement during the programmed task.
The adaptive control of a complex mechanical structure, such as a robot, requires the measurement of the physical forces produced during the gripper movement and/or object manipulation. These forces can be broken down into two main categories:
- Kinematic forces, such as those exerted on the wrist assembly by the acceleration of the object mass during a move operation.
- Static forces, such as those exerted by the gripper on to the object surface during a manipulation operation.
This latter category has further led to the development of force sensors used within the gripper and which, because of their human analogy, are called tactile sensors.
Force Measurement Generalities
Force transducers perform the mechanical-to-electrical energy conversion by measuring the physical deformation that the force in question has produced on the transducer.
Figure 1 Direct measurement, force deforms transducer only
This deformation can be caused directly, as shown by Figure 1, or more commonly transmitted to the transducer via a support material, as shown in Figure 2. The choice and shape of the support material in the latter case greatly affects the performance of the force transducer, in particular its dynamic measurement range. The long-term stability of the support material and its adhesion to the transducer itself also affect the measurement and require consideration when designing a force transducer system.
Figure 2 Indirect measurement, force deforms both support and transducer
The direct measurement method shown in Figure 1 is used mainly in tactile sensors. The indirect method of force measurement via a support material will be assumed throughout the rest of this chapter, therefore a brief description of the influence of the supporting structure on the force measurement is required. There are three main types of force which the transducer needs to measure: traction/compression, bending and twisting force.
1. Traction/Compression Force Measurement
This force, as illustrated in Figure 3, is applied longitudinally to a support structure such as to cause an increase (for traction) or decrease (for compression) of its length ±ΔL; an example of a structure under traction stress is one of the limbs of the robot in the vertical position. The physical deformation ΔL produces a change in the transducer unstressed parameter value Vt in accordance with a constant of proportionality K: 
Figure 3 Traction/compression force measurement principle
The unit change in the transducer parameter value (ΔVt/Vt) is the quantity usually measured. The force applied can be obtained if the supporting structure cross-sectional area A, its Young’s modulus E and the transducer’s sensitivity Gf are known, as shown by eqn (1), Young’s modulus being the ratio E = (stress/strain)
The unit change in the transducer parameter value (ΔVt/Vt) can be measured using a variety of techniques, some of which will be described later in this chapter.
2. Bending Force Measurement
Figure 4 Bending force measurement principle
A bending force can be defined as that which causes a longitudinal flexion in a support structure, as illustrated in Figure 4. An example of structure subject to a bending force is a robot limb in a non-vertical position with a mass suspended at its free end (which can be either the object mass or, as in this case, the robot next limb), as illustrated in Figure 5. Having measured the unit change in the transducer unstressed parameter (ΔVt/Vt), the flexing moment Mf can be obtained as shown in eqn (2).
Figure 5 Example of robot limb subject to bending force caused by weight of forearm and gripper
where W is the stiffness of the support structure to a bending force, E is its Young’s modulus and Gf is the transducer sensitivity.
3. Twisting Force Measurement
This force, as the name suggests and Figure 6 illustrates, is present in all rotating structures, such as the drive shaft of a robot actuator. The measurement of the twisting force on such a shaft may, for instance, be required to monitor the mechanical resistance to the shaft rotation. The twisting moment Mt can be derived as shown in eqn (3): 
Figure 6 Twisting force measurement principle
where St is the tangential stiffness of the shaft, d is the shaft diameter and Ip is the moment of polar inertia of the shaft cross-section which, for a cylindrical shaft, is given by 0.1 d4; (ΔVt/Vt) still represents the measurement of the unit change in the transducer parameter value.
Force Transducers Generalities
There are three main types of force transducers: resistive, semiconductor (also sometimes called piezoresistive) and non-resistive. The last, which includes capacitive and fibre-optic types, do not find many applications within a robot structure but can be used in some of the peripheral systems and have therefore been included in this chapter. Resistive and semiconductor transducers are generally referred to as strain gauges.
