**2.1. Structure of the** *Osaka Hand*

A general overview of the system is shown in Figure 1. An exceptional feature of the *Osaka Hand* is that the user can control voluntarily the angle of its fingers and the stiffness of the grip (the resistance that the fingers oppose to change their angle) by the EMGs of flexor and extensor muscles of the wrist (see details in Akazawa *et al.*, 1987).

To obtain such a control, the *Osaka Hand* mimics the properties of both muscle viscoelastic‐ ity and the gain of the stretch reflex (both varying linearly with muscle activity). The dynamics of this neuromuscular control system were determined by analyzing the tension responses of finger muscle to mechanical stretch (Akazawa *et al.*, 1999). The dynamics are quite complex, due to the non-linearity and time delay of the stretch reflex; however, we used a simple model representing the dynamics as a first approximation. Once that model was introduced in the prosthetic hand, it was proved that a sound-limbed subject and an amputee subject were able to accurately control finger angle and stiffness of the prosthet‐ ic hand (Okuno *et al.*, 1999).

As shown in Figure 1, for each subject a pair of surface electrodes were put on the *flexor carpi radialis* (wrist flexor muscle) and another pair on their *extensor carpi radialis brevi* (wrist extensor muscle) to measure their EMG signal. The measured signal was amplified in differential mode, full-wave rectified, and then smoothed with a low-pass filter to obtain its envelope, the amplitude of which is approximately proportional to the force exerted by the muscle (Basmajian and Deluca, 1985). Therefore, the resultant signal corresponded to the isometric contractile force (torque) of each muscle: *Af* being the torque of the flexor muscle, and *Ae* the torque of the extensor muscle.

From those two calculated torques, the desired finger angle *<sup>Θ</sup>*˜ *<sup>H</sup>* of the end effector (the target angle the user wants to achieve) was calculated as

$$\tilde{\Theta}\_H(\mathbf{s}) = \{P\_H(\mathbf{s}) + A\_\varepsilon(\mathbf{s}) - A\_f(\mathbf{s})\} / G\_x(\mathbf{s})\tag{1}$$

where *PH* is the grip force exerted by the fingers of the *Osaka Hand*, and was measured by strain gauges (KYOWADENGYOCo.,Ltd.(Yokohama,Japan),modelKFG-1N)attachedtoits thumb, index, and middle fingers. *Gx*(*s*)is the transfer function that represents the dynamics of human neuromuscular control system (Akazawa *et al*., 1987; Okuno *et al*., 1999), and is given by:

$$\mathcal{G}\_{\chi}(\mathbf{s}) = \mathcal{K} \frac{1 + \tau\_2 s}{1 + \tau\_1 s} \tag{2}$$

**2.2. Composition and operation of the simulator**

Inset: detail of LED markers attachment.

Figure 2 shows the components of the simulator system, which can be divided into three main sub-systems: data acquisition (EMG and video), processing, and display. Ten light emitter diode (LED) markers and two pairs of surface electrodes are attached to the subject's upper limb as shown in Figure 2(a) and 2(b). Those LEDs and electrodes provide the inputs for the processing sub-system, which is implemented in the graphic workstation (Figure 2(c)).

Simulator of a Myoelectrically Controlled Prosthetic Hand with Graphical Display of Upper Limb and Hand Posture

http://dx.doi.org/10.5772/55503

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**Figure 2.** Overview of the simulator components. The graphic workstation (GW) receives the 3D location of the LED markers (a) attached to the subject's arm and the processed EMG signals from two surface electrodes placed on the subject's forearm (b). From these data, the GW calculates and displays (c and d) the finger angle and the arm posture.

Figure 3 shows the block diagram of the simulator, illustrating how the processing system (Figure 3(c)) determines the position of the upper limb from the three-dimensional (3D) location of the markers on the shoulder, elbow, and wrist detected with an OPTOTRAKTM 3D camera (NORTHERN DIGITAL Inc., Ontario, Canada) (Figures 2(a) and 3(a)). The processing system determines the desired finger angle from the processed surface EMGs of both wrist

where the time constants were calculated to be *τ*<sup>1</sup> =0.12*s* and *τ*<sup>2</sup> =0.25*s*, and the gain *K* corresponds to the stiffness of the prosthesis fingers, which is not constant, but time-varying as:

$$K(t) = K\_0 + a \left[ A\_f(t) + A\_e(t) \right]\_{\prime} \tag{3}$$

in proportion to the contraction level of the extensor-flexor muscles pair. The user can regulate the stiffness of the hand fingers angle by varying the level of contraction of each of those muscles. The stiffness at resting state *K*0 is 0.1 Nm/rad, and the coefficient *a* is 0.98 rad-1. A software program implementing this model was introduced in the microprocessor that controls the end effector.

The position control system (see Figure 1) consists of a DC motor (MINIMOTOR SA, Cro‐ glio, Switzerland, type 2233), its servo controller (Figure 1(c2)), and a one degree-of-freedom end effector with three fingers (Figure 1(c3)). Index and middle fingers are bound between them and are endorsed with an open-close movement with respect to the thumb. This move‐ ment is produced by the DC motor, the servo controller of which works to nullify the differ‐ ence between the commanded angle *<sup>Θ</sup>*˜ *<sup>H</sup>* and the actual motor rotational angle *Θ* ^ *<sup>H</sup>* as measured by an optical encoder.

**Figure 1.** Block diagram of the *Osaka Hand*. The model of the human neuromuscular control system dynamics (labeled as c1) takes the processed EMG signals *Ae* and *Af* from the subject's forearm and calculates the target angle Θ˜ *<sup>H</sup>* ; the servo controller (c2) works to nullify the difference between Θ˜ *<sup>H</sup>* and the actual motor rotational angle <sup>Θ</sup> ^ *<sup>H</sup>* . The end effector (c3) has one opening-closing degree-of-freedom Θ*<sup>H</sup>* .
