Walking Step-By-Step Swing Leg Velocity Measurement

Xiang Zheng Tu

More and more people believe that they never avoid becoming completely old, but they may delay the time becoming old. They may look younger when they are 70 and may live into their nineties. This may be true if they pay attention to personal health care and increase the amount of physical activities such as walking and running in daily life. Research shows getting up and walking around for two minutes out of every hour can increase your lifespan by 33 percent, compared to those who do not. According to the UK’s National Health Service (NHS), the average person only walks between 3,000 and 4,000 steps per day, but aiming for 10,000 steps is a better goal.

Therefore, it necessary for the people to know how many steps they walk or more practical how much calories they consume. So many pedometers have been developed. A sophisticated pedometer likes a swinging pendulum-hammer and measures steps with two or three accelerometers. A microchip is arranged at right angles that detect minute changes in force as a people move his legs. Since accelerometers are often built into gadgets like cell phones, it's increasingly common to find these sorts of pedometers. 

Counting steps with a pedometer based on inertial measurement units (IMUs) sounds super-scientific, but you need to remember that it's only an approximate measurement. Not all steps will be correctly counted and some false movements such as jolts in the road as people ride in a car might be counted as steps too. Don't take the count too seriously; assume that it's in error by least 10 percent.

IMUs can only be used for counting step number but not for measuring step length. Weiwei et al subjected that the swing leg moves at a constant speed, the energy cost of swing foot movement is inversely proportional to the step length. The fact is that step length varies from person to person and also varies for the same person when walking or running at different speeds. So without step length it is impossible to calculate the calories consumption precisely.

According to Kuo et al’s assumptions, the energy or calories E consumed in a leg swing during human walking has a component corresponding to the cost of pushing off with the stance leg (i.e., toe-off) E_toe, and a component corresponding to forced motion of the swing leg, E_sming. The energy E can be expressed as

E = E_toe + E_swing ~ω^-1 υ³ +c ω^k-λ υ^2λ,   (1)

where ω is the swing leg natural frequency, υ is the swing leg velocity, c is the relative proportional between E_toe and E_swing, κ and λ are the metabolic cost exponents. The swing leg natural frequency ω related to the swing leg speed υ by a simple approximation as

υ ~ ω^1/2 p^1/2,    (2)

where p is the toe-off impulse which is applied heel strike. From equations (1) and (2), the calories consumption E at a given walking step is mainly determined by the swing leg velocity υ. It seems that to get more accurate calories consumption E needs to measure the swing led velocity directly.

Direct calories consumption measurement can be done using a new type of pedometers provided by the present author. The new pedometer uses three thermal motion sensors to measure the linear velocity of each swing leg trajectory at human walking or running. As shown in the above figure, a man is walking across the paper. His legs swing through the space resulting in two curved paths which are called swing leg trajectories. The blue one is the right leg swing trajectory and the red one is the left leg swing trajectory. Each trajectory can be divided into two sections: the first or up section and the second or down section. Three thermal motion sensors are attached to the right shoe of the walking man and arranged to be along with y+, x+ and y- axis of a sensor coordinate system respectively. The sensor coordinate system is tracking the right swing leg trajectory. In the up section of the trajectory the linear velocity υ_up of the swing right leg motion is located in the first quadrant of the sensor coordinate system and its y+ component υ^y+_up

and x+ component υ^x+_up can be measured by y+ motion sensor and x+ motion sensor , respectively. In the down section of the trajectory the linear velocity υ_down of the swing right leg motion is located in the forth quadrant of the sensor coordinate system and its y- component υ^y-_down and x+ component υ^x+_down can be measured by y- motion sensor and x+ motion sensor, respectively. Understood that for any right triangle the side lengths and hypotenuse are related by the Pythagorean theorem:

υ​²​​ = υ​_x​​​²​​ + υ​_y​​​²​​.     (3)

The magnitude of the linear velocity υ can be found simply by taking the square root.

The measured linear velocity is an instant velocity of a swing leg movement. A walking step length can be calculated by integration of the measured instant velocity. Each walking step is performed with the following actions:

·      Lift one leg off of the ground,

·      Using the leg in contact with the ground, push your body forward,

·      Swing your lifted leg forward until it is in front of your body, and

·      Fall forward to allow your lifted leg to contact the ground.

The start and the end velocities are always zero, since at these points the leg should be in contact with the ground. So the integration is a definite integral witch is limited by an interval between the start zero and the end zero. In the definite integral the answer does not have any constants such as an infinite integral. This means that the walking step length can be determined by integration of the linear velocity without need extra information.

The thermal motion sensors measure the linear velocity of the swing leg movement is based upon the concept of convective head transfer. Each thermal motion sensor comprises of a thermal insulated base recessed into and surrounded by a silicon chip. A heating resistor and the hot junctions of a thermopile display on the surface of the base. The cold junctions of the thermopile display on the surface of the silicon chip near the base edge. The sensors are attached to a shoe and move forward with the swing leg of a walking man. The heating resistor is heated to maintain a continuous overheat between the resistor and the flowing air over the surface of the sensors. The thermopile is functioned as a temperature sensor. Both the actuations are performed by a POSIFA proprietary integrated circuitry. As air flows by the heated sensors, flowing air molecules transport heat away from the sensors and as a result, the sensors cool and the heat is lost. The circuit balance is disrupted, and the temperature difference between the heated resistor and the air is produced. The temperature difference is measured and converted to the data representing the velocity of the sensors movement.