## EXSS 323 CENTER OF MASS LAB

• ### INTRODUCTION

Determination of the body's center of mass is an important part of most biomechanical analyses. In previous lab work, you may have used a balance board method to determine the center of mass location for a static situation. While this is an accurate and straight forward method, it is not practical for analyzing an activity with a range of body positions. For such an analysis, an alternative approach is to determine the center of mass location from an image of the motion at some point or points in time. This might be done from a printed photo or from a series of frames of cine film which record a complete movement pattern. In either case, the technique involves using the segmental positions of the body and estimates of the segmental masses and center of mass locations. The details of this approach are outlined below.

• ### METHODS

The center of mass is an ideal point about which the torques due to body segment weights is zero. It can be determined in the following manner:

1. Choose some arbitrary reference point as origin of the coordinate system to be used.
2. Determine the center of mass location of each segment of the body (an X, Y pair of coordinates).
3. Calculate the torque about the reference point due to each segment (based on the segment's mass and position).
4. Sum the torques about the reference point for all the segments (one sum for X direction, one for Y direction).
5. Divide the sum of the torques by the total body mass to determine the center of mass location with respect to the reference point.

This method is based on the idea that the torque about the reference point due to the whole body is equal to the sum of the torques about the reference point due to the body segments. In short, the method can be summarized in the equation:

where M is mass, X is a position coordinate and n is the number segments.

In applying this method to real situations, anthropometric information about human body segments is used to determine the location of each segment's center of mass and each segment's mass. Each of these body segment parameters (BSP) is usually expressed as a percentage value. In the case of location of the segment's center of mass, it is described as a percent of segment length from the proximal end. In the case of segment mass, it is described as a percent of total body mass. Such BSP data come from cadaver studies performed in various labs during the past century. The most frequently cited of these studies are those of Dempster (1955) and Clauser, McConville and Young (1969), which are based on cadaver dissection studies. One frequently cited source of BSP's was published by Plagenhoef et al (1983). Summaries of these studies are included in many textbooks (e.g., Hamill & Knutzen, 1995, pp. 431-435).

Another source of BSP's is from radioisotope absorption studies carried out in the 1980's in the former Soviet Union (Zatsiorsky, Seluyanov, & Chuganova, 1990). Adjustments to Zatsiorsky et al were published by Paolo de Leva (Journal of Biomechanics, 29(9), pp.1223-1230, 1996) to make the data easier to use. As the Zatsiorsky et al data were derived from young, athletic subjects (instead of cadavers of old white men), they are considered more representative of the BSP's of young people. Estimates of BSPs for young males and females from de Leva (1996) are included herein.

As an example of how these body segment parameters are used, consider a male's thigh segment located as illustrated in the figure  (in this example only, the data from Plagenhoef et al are used; you will use the de Leva data for this week's lab). If this person's whole body mass was 80 kg, the thigh mass can be determined as a percent of 80 kg, ie. 10.5% of 80 = 8.4 kg (where 10.5% is the thigh segment mass percent from Plagenhoef).

The thigh center of mass location can be determined from the proximal and distal point coordinates and the segment length percent. If for the thigh the center of mass is located at about 43.3% of the length from the proximal end, the specific coordinates can be determined as follows:

Segment CM X Position = X proximal + (Length %) (Xdistal - Xproximal)

Xthigh = 10 + (.433)(70 - 10) = 35.98

Ythigh = 30 + (.433)(40 - 30) = 34.33

The red dot marks this location of the thigh segment center of mass.

### Example for Determining Whole Body Center of Mass

Whole body center of mass determination is based upon knowing segmental center of mass locations which in turn are based upon segmental end point positions.

### Procedures for this lab:

• On a relatively large picture of a human in action, determine locations of the following anatomical landmarks: toe, heel, ankle, knee, hip, shoulder, elbow, wrist, third knuckle (MCP), C7-T1 and top of head. For data collection, a printout of a data table will simplify recording of coordinate information. Use the attached picture of a Gymnast for your analysis.
• Enter the segment end point coordinates into a spreadsheet. Combined with segment length percents, determine segment CM locations.
• Using segmental mass percents, determine torque for each segment.
• Sum the torques for all the segments and determine the whole body center of mass location.
• Printout your spreadsheet results. Return to the picture you have analyzed and locate where on the image the whole body center of mass is located using the computer image coordinates. Mark this point on a printout of the picture.
• ### SUMMARY REPORT:

Based on your data collection, analysis and results, briefly summarize the procedures used to determine whole body center of mass. In addition, discuss the specific image used in the lab and how center of mass relates to such performance. In your summary and discussion, include responses to the following questions. Attach printouts of your spreadsheet and picture to the written paper and return these to your lab instructor at the beginning of the next lab meeting.

1. For the body configuration analyzed, was the calculated center of mass position within the volume of the body? Under what configurations would you expect the center of mass not to be within the volume of the body?
2. Was the calculated center of mass position over the base of support in the photo analyzed? Under what conditions does the center of mass have to be over the base of support and when does it not have to be?
3. The process of estimating the center of mass location based on body segment parameters (the segmental masses and locations) introduces some estimation errors into the calculations. What errors were involved in this whole process? Which are the most significant errors?