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 suspension 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.

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). Summaries of these studies are included in many textbooks. Your recent reading of Plagenhoef (1983) made use of part of Dempster's study combined with measurements on young adults to estimate BSPs for young males and females.

As an example of how these body segment parameters are used, consider a male's thigh segment located as illustrated in the figure. 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:

Example for Determining Whole Body Center of Mass

• First, determine each segment's end points.

• Then, use the endpoint coordinates to determine segment center of mass coordinates.

• Combine these segment coordinates with segment masses to determine each segment's torque about some reference point (the origin).

• Finally, use total torque to determine Whole Body center of mass location.
  
  

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, finger tip, C7-T1 and top of head. For data collection, open this excel template to record 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.

  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).
  
  

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.As part of 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. Discuss what errors were involved in this whole process. Which are the most significant errors?