Visual Speed feedback system

In order to provide visual feedback to allow the person to propel the wheelchair at the required speed during a wheelchair propulsion test (Fig.2.4), an independent visual speed feedback system was developed and calibrated.

Figure 2.4. Diagram of the ergometer and wheelchair.

2.1.2.1 Speed Sensors Tachometer

A D.C. tachometer generator, which converts rotational speed into an isolated analog voltage signal, used to measure the rollers’ rotation speed (Fig. 2.5).

The wheelchair is propelled by the person sitting in it, who applies manual force to the wheel. Force is then transmitted by the wheel to the roller it sits on. The roller in turn imparts force to the wheel mounted on the tachometer shaft. The tachometer, which thus rotates at the same angular velocity as the wheelchair wheel, generates a

voltage in direct proportion to that angular velocity. Wheelchair angular speed is demonstrated in units of voltage.

Figure 2.5. D.C.Tachometer and tachometer wheel.

The wheelchair is propelled by the person sitting in it, who applies manual force to the wheel. Force is then transmitted by the wheel to the roller it sits on. The roller in turn imparts force to the wheel mounted on the tachometer shaft. The tachometer, which thus rotates at the same angular velocity as the wheelchair wheel, generates a voltage in direct proportion to that angular velocity. Wheelchair angular speed is demonstrated in units of voltage.

Magnetic field sensor

To measure linear speed and calibrate the reading of the tachometer voltage output, two magnetic field sources (magnets) were attached near the rim of the roller (Fig.2.6), so that the resolution could be counted with a magnetic field sensor. The magnetic field sensor was mounted on a stationary arm close to the rim of the roller (Fig. 2.7). As the magnets rotate past the sensor, the occurring electric spikes were recorded. The distance between two magnets is known, and the travel time between two magnets was calculated by peak to peak pulse with known a sampling rate. So the linear speed was calculated by:

V = d / t

d is the distance between the two magnets t is the travel time between the two magnets.

-0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.002 0.042 0.082 0.122 0.162 0.202 0.242 0.282 0.322 Time (Second) V o lt a g e (V )

Figure 2.6. Two magnets are attached on surface of the roller. The distance between the two magnets is 10cm (left). A pulse is generated when the magnet is passing by the magnetic field sensor (right).

Figure 2.7. The magnetic field sensor is taped on the bar that is mounted flush against the roller

2.1.2.2 Data acquisition

The output wires of the tachometer and magnetic field sensor were connected to a 12-bit Analog to Digital Converter (PCI ST300, Data translation, UK). The data acquisition was carried out in LabVIEW (National Instruments). The tachometer and magnet data were sampled at 500 Hz. The configuration of the program is shown in Fig.2.8.

Figure 2.8. Front panel of LabVIEW program used to record the signals from magnetic field sensor and tachometer. A single ended channel was use, and the sampling rate was 500Hz per channel.

2.1.2.3 Protocol

The deceleration or "coast-down" test was done manually accelerating the roll to a steady-state speed, and then removing the input while recording the speed as a function of time as the device decelerates to zero. Therefore, the rollers were animated up to a high velocity and then the system was allowed to decelerate to a complete standstill. During this period, the output voltage signal of the tachometer and the output spike signal of the magnetic field sensor were recorded

simultaneously (Fig.2.9). -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1 222 443 664 885 1106 1327 1548 1769 1990 2211 2432 2653 2874 3095 3316 3537 3758 3979

Magnetic field sensor tachometer

Figure 2.9. The output voltage signal of the tachometer and the output spike signal of the magnetic field sensor were recorded simultaneously.

Because of differences between the right and left side of the system, the roller speed was recorded separately for right and left. The velocity and voltage were used in conjunction with a linear regression analysis in order to determine the system parameters for the visual speed feedback.

So the conversion of voltage and speed was based on: Y = mx + b m – Scale b – Offset y = 0.8086x + 0.0175 R2 _{= 0.9968} 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.5 1 1.5 2 2.5 Voltage(V) S p e e d (m /s ) Series1 Linear (Series1) y = 0.7344x + 0.0313 R2 _{= 0.9982} 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 1.5 Voltage(V) S p e e d (m /s ) Series1 Linear (Series1)

Figure 2.10.The regression line of roller speed and tachometer voltage. Left roller (left), Right roller (right)

According to rotational theory, if v represents the linear speed of a rotating object, r its radius and ω its angular velocity in units of radians per unit of time, then

v = rω

The linear speed of the roller is the same as that of the tachometer wheel. Since the tachometer shaft is attached directly to the tachometer wheel, it rotates exactly as the tachometer wheel does: every full revolution of the tachometer wheel means a full revolution of the shaft. Since the output voltage is proportional to the angular speed of shaft, there also is a linear relationship between the linear speed of roller and the output voltage (Table 2.1).

Table 2.1. Rotational-Linear Parallels

Linear motion Rotational motion

S Arc length

rg Radius of gyration

Position x θ Angular position

Velocity v ω _{= v/rg} Angular velocity

Acceleration a or at (tangential

acceleration)

α _{= at/rg} Angular

v = vo+at ω = ωo+ αt x = vot + ½at2 θ = ωot + ½αt2 v2 = vo2 + 2ax ω2 = ωo 2+ 2αθ Mass (linear inertia) M I Moment of inertia

Newton’s 2nd law F = ma τ _{= Iα} Newton’s 2nd law

Momentum P = mv L = Iω Angular

momentum

Work Fd τθ Work

Kinetic energy ½mv2 ½Iω2 Kinetic energy

Power Fv τω _Power

The resulting speed, as recorded by the tachometer and then calibrated by linear regression analysis, was compared with the speed recorded by the SmartWheel to ensure the two recording systems matched each other (Fig. 2.11). There was a close match for both measured speeds.

The coefficients used to calculate the visual speed feedback: Left roller: V * 0.81 + 0.0175

Right roller: V * 0.76 + 0.0201

V - Voltage recorded by the tachometer. Speed recored by tachometer

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1 132 263 394 525 656 787 918 1049 1180 1311 1442 1573 1704 1835 1966 2097 S p e e d (m /s )

Speed recorded by Smartwhell

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1 349 697 1045 1393 1741 2089 2437 2785 3133 3481 3829 4177 4525 4873 5221 5569 S p e e d ( m /s )

Figure 2.11. Speed recorded by the tachometer (left) and the SmartWheel (right).

Once the calibration coefficients were determined, A LabVIEW program was coded for providing the visual speed feedback.

Figure 2.12. A monitor with the LabVIEW program was set in front of the wheelchair to provide visual feedback.

Braking force of roller at constant velocity with no added resistance F = ma

From roller data

Regression of speed m/s vs sample number = 0.0014 Left = 0.7m/s/s Regression of speed m/s vs sample number = 0.0006 Right = 0.30m/s/s

F = 32.37 x 0.32 = 9.7N (Right) and 22.7N (Left) Total rolling resistance = 32.4N