*2.2.2. Processing system*

flexor and extensor muscles of the subject (Figures 2(b) and 3(b)). The virtual upper limb and hand are ultimately presented on the 3D graphic workstation (display system, Figure 3(d)).

**Figure 3.** Simulator block diagram. With the 3D markers position obtained from the Optotrak 3D camera (block a), the processing system (c) calculates subject's arm posture and wrist rotational angle. From the processed EMG signals *Ae* and *Af* (b), the model of the human neuromuscular control system dynamics (c1) calculates a first approximation of the desired angle Θ˜ *HS* . The dynamics of the servo control system (c2) can be regarded as the identity, Θ˜ *HS* <sup>=</sup><sup>Θ</sup>

The OPTOTRAK 3D camera (Figure 2(a) and Figure 3(a)) detects the position of the LED markers attached to the user's shoulder, elbow, and wrist. The marker on the shoulder is attached to the point where the movement of the *acromion* of the scapula is smallest during the motion of the arm. The marker on the elbow is fixed in the external palate of the humeral. The

To measure the rotational angle of the wrist during an external pronation of the arm, eight LEDs are placed on the external side of a bracelet-like device attached to the wrist (shown in

The EMG signals of wrist muscles are picked up with surface electrodes (Figure 2(b) and Figure 3(b)). These signals are then amplified (gain 58.8 dB, CMRR 110 dB) to the range ±5 V, fullwave rectified, smoothed with a second order low-pass filter (cut-off frequency 2.7 Hz), and then sampled at a frequency of 25 Hz, 12 bits per sample (resolution of ±2.4 mV, less than 0.01% of the maximum value) with an OPTOTRAK Data Acquisition Unit (NORTHERN DIGITAL

^

linear characteristics of the relationship between Θ

arm posture is calculated from those LEDs locations.

hand are displayed in the display system (d).

274 Electrodiagnosis in New Frontiers of Clinical Research

*2.2.1. Data acquisition system*

the inset of Figure 2).

Inc., Ontario, Canada).

^ *HS* . Non‐

*HS* and Θ*HS* are inserted in block c3. The virtual arm and prosthetic

The location of the LEDs and the processed EMG signals are collected by a graphics worksta‐ tion (GW, SILICON GRAPHICS, Inc., California, USA) that holds the processing system software (Figure 2(c) and Figure 3(c)).

The angle that the user wants to achieve with the prosthesis fingers (the target angle) is given by Eqs. (2) and (3) using the current value of user's EMG signals *Ae* and *Af* . Those equations are calculated in the real *Osaka Hand* by a Z-transform that gives in discrete time their solution, originally expressed in the frequency domain (see Figure 3(c1)). In the case of the processing system of the simulator, the sampling frequency is not high enough to allow using that transform. Therefore, we used the Runge-Kutta-Gill approximation method for differential equations in order to implement the transfer function *Gx*(*s*) (Eqs. (2) and (3)).

Dynamics of the DC motor servo system of the actual prosthetic hand were calculated in terms of the relationship between target angle *<sup>Θ</sup>*˜ *<sup>H</sup>* and rotational angle *Θ* ^ *<sup>H</sup>* of the motor shaft (see Figure 1). In the steady case, we assumed *Θ* ^ *<sup>H</sup>* <sup>=</sup>*<sup>Θ</sup>*˜ *<sup>H</sup>* , with zero time delay (Figure 3(c2)).

In order to model the relationship between *Θ* ^ *<sup>H</sup>* and final finger angle *ΘH* of the real *Osaka Hand* (see Figure 1), we performed the following measurements by attaching two LEDs to the prosthesis chassis and one on each fingertip as shown in Figure 4. The hand finger angle *Θ<sup>H</sup>* was defined as the angle formed between the vectors *M*1*M*<sup>3</sup> → and *M*1*M*<sup>4</sup> →, *i.e.*, the angle between the fingertips with respect to the chassis. The operation range of this angle is from 0o to 110o . The relationship between *Θ* ^ *<sup>H</sup>* and final finger angle *ΘH* (see Figure 1) was modeled with a piecewise approximation calculated by a least squares method. The error was always below 8% with an average of 1.7%, standard deviation (s.d.) 1.36. We roughly divided the operation range into three areas, as shown in Figure 3(c3).

**Figure 4.** Finger angle Θ*H* is defined as the angle formed between the vectors *M*1*M*<sup>3</sup> →and *M*1*M*<sup>4</sup> →. M1 to M4 are LED markers attached to the prosthetic hand.
