## EXSS 323 LINEAR KINEMATIC ANALYSIS

### ·         INTRODUCTION

The purpose of this lab is to provide you with experience in using video analysis techniques to analyze the linear kinematics of a movement task. Video analysis is used for many different reasons in biomechanics. It can be used to measure the release velocity during a baseball pitch, the duration of ball-foot contact during a kick, or a sprinter's acceleration coming out of the blocks. In today's lab, you will track motion during a standing long jump. Horizontal and vertical positions, velocities, and accelerations of a point approximating the body center of mass will be determined as a function of time.

In performing a video analysis, the movement task of interest is first recorded as a set of discrete images (frames) using a video camera or high-speed camera. When later analyzing the video or film, the images are typically viewed on a computer monitor, projected onto a screen, or printed to paper. The images may thus be smaller or larger than real-life size. Because the images are seldom used at real-life size, any distance measured on the image must be multiplied by a constant calibration factor to convert it to its real-life value.

The standard procedure for determining the calibration factor is to place a meter stick in the camera's field of view during the filming. Knowing the calibration stick's real length and its length when projected, a constant calibration factor can be calculated with the following formula:

For example, if a 1 meter calibration stick was placed in the field of view during filming of a runner and then measured as 8 millimeters in the image that was projected from the film, the conversion factor would be:

The CF is used to convert distances measured in millimeters on the projected image to real-life distance in meters. For instance, if a runner moved 64 mm from beginning to end of a set of images, the real-life displacement (d) would be obtained by:

`Notice that the units cancel to yield a displacement in meters.`

It is often necessary to be able to determine the elapsed time between events when analyzing video or high speed film. For example, if average running velocity is to be calculated from film images, time is in the denominator of the velocity equation (v = d / Δt). Measuring the time can be accomplished by knowing the number of frames between two events of interest and the time per frame.

High-speed film cameras usually have adjustable frame rates that are frequently set to shoot at 50 – 200 frames per second (f/s). Video recording is less adjustable. Images can usually be analyzed at 60 or 30 f/s. In general, more rapid movements should be filmed at higher frame rates.

The time interval between each frame of film or video and the next can be calculated from the camera speed setting. For example, if a camera speed of 100 f/s is used, the time between frames is:

This time constant (0.01 seconds per frame) can then be used to calculate the time between events. For example, if the above runner (filmed at 100 f/s) took 200 consecutive frames to displace the 8 meters, then the elapsed time (Δt) would be calculated in the following manner:

From the displacement and the elapsed time, the runner's average velocity can be calculated:

While the average velocity over a period of time is often of interest, sometimes the velocity at a specific instant is of greater importance, particularly if one wishes to compute the acceleration over a period.  To find the instantaneous velocity in the X direction (vX) in frame i, one typically uses the central difference method:

vX(i )

where x(i + 1) and x(i – 1) are the X positions in frame i+1 (= 1 frame into the future) and frame i – 1 (= 1 frame into the past), respectively.  t(i + 1) and t(i – 1) are the times corresponding to frames i+1 and i – 1 and are found by multiplying the frame number minus 1 by the time per frame (tF).  A similar formula is used to compute the instantaneous velocity in the Y direction from the Y position data.  Note that, with this method, the instantaneous velocity cannot be computed for the first and last frames of data.

Once one has determined the instantaneous velocity in the X direction at different instants, one may compute the average acceleration in the X direction over a period of time (=ΔvX / Δt) or the instantaneous acceleration in the X direction at specific instants.  To find the instantaneous acceleration in the X direction (aX) in frame i, one can again use the central difference method:

aX(i )

Equivalent processing can be performed to find the accelerations in the Y direction.

### ·         METHODS

A video recording of a long jump has been included for your viewing of the movement pattern (NOTE: this file requires Quicktime MoviePlayer). Sixteen frames from the jump have been saved as individual images for analysis. These were recorded at 15 frames per second.

Links to the jump images (below) will bring up a new page with the image included. Images displayed on a computer monitor are composed of very small dots that are referred to as "pixels." The images that you will be analyzing are smaller than real-life size and are scaled at 110 pixels per real-life meter.

### Jump frames:

 1.      jump picture 2.      jump picture 3.      jump picture 4.      jump picture 5.      jump picture 6.      jump picture 7.      jump picture 8.      jump picture 9.      jump picture 10.  jump picture 11.  jump picture 12.  jump picture 13.  jump picture 14.  jump picture 15.  jump picture 16.  jump picture

For the analysis, configure a set of spreadsheet columns as illustrated in this example table.

Within the spreadsheet, use the frame numbers and frame rate to determine the time corresponding to each of the 16 frames.

Measure the horizontal and vertical position of the hip marker in each jump frame. To measure the position of the hip marker, use the mouse cursor to point to the marker. You will notice that, at the bottom of the page, a pair of numbers will be shown. These are the image coordinates of the cursor. Record these hip marker coordinates in the spreadsheet.

NOTE: This technique for finding coordinates works on the web browser installed on the lab computers and on some but not all other web browsers. If, on your browser, the coordinates do not show up in the status bar at the bottom of the page, click on the image. The page will be reloaded and the coordinates will show up at the end of the location bar (with the URL or address).

An unusual characteristic of the computer image coordinates that you have recorded is that the vertical coordinate increases as one goes down the image. This is opposite from the "normal" rectangular coordinate system used in mechanics, where up is taken as positive. We can easily convert the vertical data to a conventional system by writing a formula in the next column of the spreadsheet. The images you have analyzed had 240 pixels vertically. To set the origin at the bottom left corner, as is typical, simply subtract the measured vertical coordinate from 240: (240 - Vert Coord).

Next in the analysis is to convert from pixels to real-life dimensions in both the horizontal and vertical directions. Use the conversion information described above (1 m = 110 pixels) to determine the calibration factor. Then write a formula in the spreadsheet for new columns of real-life horizontal and vertical positions (X and Y).

Calculate the instantaneous horizontal and vertical velocities (Vx and Vy) across time using the central difference formula in the next two columns of the spreadsheet (NOTE: You will only be able to compute the instantaneous velocities for frames 2-15. Do not enter velocities for frames 1 or 16).

From the computed velocities, use the central difference formula to calculate the instantaneous horizontal and vertical accelerations (Ax and Ay) across time in the last two columns of the spreadsheet (NOTE: You will only be able to compute the instantaneous accelerations for frames 3-14. Do not enter accelerations for the other frames).

Finally, to display your results, create graphs of:

·         position vs. time

·         velocity vs. time

·         acceleration vs. time

for the jump. On each graph, include both the horizontal and vertical components.