**4. Tendon excursion**

Tendon excursion is often thought of as a limiting factor in electromechanical hand design. Tendon excursion is the displacement an artificial tendon experiences when the associated muscle/actuator contracts and induces tensile forces on it. Tendon excursion is can effect hand movement negatively.

For example, wrist movement induces tendon excursion on all the FDP tendons of the fingers. This can be seen in the natural flexion of the fingers during wrist extension and their natural extension during wrist flexion (**Figure 13**).

**Figure 13.** *Tendon excursion in the FDP of each finger induced by wrist movement.*

*Biomechanical Design Principles Underpinning Anthropomorphic Manipulators DOI: http://dx.doi.org/10.5772/intechopen.105434*

The angles *ω<sup>f</sup>* and *ω<sup>e</sup>* represent the magnitude with which the wrist joint is in flexion or extension respectively. *ω* ¼ 0 is located vertically upward from the forearm bones and is measured from the pivot point of the wrist to the metacarpal creating the largest angle from the equilibrium point. In this case measurements are taken from the metacarpal of the little finger. Let us take the artificial FDP flexor tendon of each digit as an example. We can write a set of tendon displacements with respect to the wrist angle. Let, *ω<sup>f</sup>* represent wrist flexion for any *ω*>0. We can write

$$a\_f = \{d\_{\rm Fi} d\_{\rm Fm} \, d\_{\rm Fr} \, d\_{\rm Fl} \, d\_{\rm Ft} \} \tag{6}$$

Where, *d* is the displacement of the tendon in mm and the subscripts*i, m, r, l* and *t* are the index, middle, ring, little, and thumb digits respectively. The subscript, *F*, represents the flexor tendon and in the case of the thumb, *dFt* ¼ f g *dFt*<sup>1</sup> *dFt*<sup>2</sup> . Where, *dFt*<sup>1</sup> *and dFt*<sup>2</sup> are artificial replications of the the APL and FPL (**Figure 11**) tendons respectively.

The effect of tendon excursion can be quantified by measuring the elongation/ displacement flexor tendons while the wrist is moving. After measuring the artificial FDP displacement each finger was displaced by over 10 mm. A 10 mm displacement represents more than 50 percent of the fingers total motion, thus, tendon excursion cannot be ignored. In a similar manner the effect of tendon excursion on the thumb is too large to ignore, therefore we look to the following section as one solution to manage the unwanted effects of tendon excursion.

The source of displacement for each artificial tendon stems from its actuator, therefore, solutions can be found by adjusting the tendons actuator to account for the unwanted tendon excursion. Let us assume an anthropomorphic manipulator we have a series of four servomotors actuating four artificial FDP tendons. A servomotor correction factor can be implemented within the control scheme which considers the wrist angle. The correction factor allows the wrist induced excursion to meet equilibrium with the individual finger servomotors during wrist movement using:

$$
\sigma = \left(\frac{\pi R}{180}\right) \times \rho\_i \tag{7}
$$

Where, *R* is the servo horn radius and *φ<sup>i</sup>* is the angle of the servo horn. By so doing, the servomotor angles for each digit can be plotted against the wrist angle, *ω* at any given time.

**Figure 14.** *Servomotor correction angles for wrist movement induced tendon excursion in the fingers.*

The excursion correction angles displayed in **Figure 14** shows how servomotor angles change with respect to wrist position.

Including these types of correction tables into the control schemes of all electromechanical anthropomorphic hands is trivial but important for hand function and control.
