## EXSS 323 CENTER OF MASS LAB

This lab was developed by Young-Hoo Kwon, Ph.D., of Texas Woman's University, and is used by permission.
Portions in italics are additions/modifications to the original and were made by Gary Christopher, M.S., A.T.C.

Introduction

Mass is defined as 'the quantity of matter composing a body'. In every object, there is a unique point called 'center of mass (CM)' around which the object's mass is equally distributed in all directions. In other words, mass is balanced at the CM in all directions.

Finding the CM of an object is an important task in biomechanics since, in many cases, the CM of an object is the point which effectively represents the whole object. Let's relate the CM with some of the issues we've been dealing with:

- Strategies to analyze the motion of an object: General motion is mixture of both linear motion (rectilinear or curvilinear) and angular motion. We can dissect a general motion into the linear motion of the CM of the object and the angular motion of the object about its CM. In this case, CM is used as the reference point in describing the angular motion of the object.

- Position, velocity & acceleration of an object: The position, velocity and acceleration of an object is in fact identical to those of its CM, respectively. We are using the CM of the object as the representing point of the object.

- Projectile motion: We know that any object thrown into the air follows a parabolic path due to gravity. (Of course, we ignore the effects of air resistance here.) Actually, the one following a parabolic trajectory is the CM of the object, not the object itself.

- Weight of an object: Weight is the gravitation acting between the earth and the object. It's direction is downward. The weight vector (force vector) passes through the CM of the object.

As you see in all these examples, CM is an important biomechanical concept. It is why we need to find the CM of an object.

Finding the CM of a simple rigid object is a simple task. Since the shape of the object does not change and there is no mass shift in this kind of object, the relative location of the CM does not change. By hanging the object in different orientations, one can easily find location of the CM.

But the human body is a system of segments linked to each other at the joints. In other words, mass distribution changes continuously as the body posture changes. As a result, the relative CM location changes continuously. It is not a simple task to find the CM of the human body. The purpose of this lab is to introduce a procedure called 'the segmental method' for finding the CM of the human body.

Methods

The Segmental Method

The segmental method involves computation of the segmental CMs (Figure 1). The whole body CM is computed based on the segmental CMs.

Figure 1. The segmental method (Adapted from Hamil & Knutzen, 1995, Biomechanical basis of human movement, Baltimore, MD: Williams & Wilkins.)

Digitizing

The first step in the segmental method is to quantify the body posture of the subject. The best way to do this is to record subject's motion and to read off the coordinates of selected body points, such as joints, from the recorded images (film or video). This process is called 'digitizing'. In this lab, you will actually go through the digitizing process. When you place your cursor at a spot on the image, the X & Y coordinates of the points will be displayed on the address bar at the bottom of the web screen.

Body Segment Parameters

Since the human body consists of several segments, such as hands, forearms and upper arms, the overall mass distribution within the body is a function of the mass distribution within the individual segments and the body posture. As explained earlier, the body posture can be quantified through the 'digitizing' process.

Mass distribution within the segments is known in the form of body segment parameters (BSPs). BSPs include body segment masses and the locations of their centers of mass. These parameters were obtained mainly from cadavers in the 50s, 60s, and 70s 1,2,4.

Research conducted in the former Soviet Union in the 1980's 5,6,7,8 provided an alternative source of BSP's. This research differed from previous research in that it was performed on young, fit, living subjects. As such, the BSP's developed by Zatsiorsky are considered (by your instructor) to be superior to those developed from cadaver research. Zatsiorsky's BSP's have not found wide use, however, due to his selection of non-standard segment endpoints. Adjustments to Zatsiorsky's data were published in 1996, 3 making them more usable. Still, old habits die hard, and many scientists still use the cadaver based data despite the availability of Zatsiorsky's BSP's. Body segment parameters we will use in this lab are provided in the attached table.

For example, the CM of the forearm (female) is located at 45.59% of the forearm length from the elbow, the proximal end of the forearm; the forearm mass is 1.38% of whole body mass.

If the location of the end points of a segment is known, one can compute the location of the segment CM using the CM location data shown in table 1 (See figure 2):

XCM = (XD)(%cm) + (XP)(1 - %cm)  -or-  (XP) + (%cm)(XD - XP) [1]

YCM = (YD)(%cm) + (YP)(1 - %cm)  -or-  (YP) + (%cm)(YD - YP)  [2]

Figure 2. Segmental CM

where (XCM, YCM) = X & Y coordinates of the segmental CM, (XD, YD) = coordinates of the distal end of the segment, (XP, YP) = coordinates of the proximal end, and %cm = CM location ratio shown in Table 1 divided by 100. Equations 1 & 2 and female BSP's are already embedded in the worksheet for the R Hand. You will need to generate the rest of the equations in your spreadsheet. You may use this example data table and figure as a reference to ensure your equations are appropriate.

Computation of the Body CM

The body CM can be computed from the CMs and the masses of the segments:

[3]

[4]

where (X,Y) = coordinates of the body CM, i = segment number, (Xi, Yi) = the X & Y coordinates of the CM of segment i, and mi = mass of segment i. In other words, the body CM coordinates are equal to the sum of the products of segmental mass and segmental CM coordinates divided by the body mass (Smi).

CM of a Gymnast in Static Balance

The Excel worksheet file will be provided. A photograph of the athlete to be digitized is provided here. Enter coordinates from the picture into the worksheet. As you proceed, you will see a stick figure shaping up in the graph window. A small 'x' will appear at the center of mass of each body segment (including the trunk). A blue dot will appear at the location of the center of mass of the whole body. Upon completion of this example, enter your names and print out the worksheet (a color printout is NOT necessary). Turn in the printout only.

There is no writeup due for this lab!!

References:

1.    Chandler RF, Clauser CE, McConville JT, Reynolds HM, & Young JW (1975). Investigation of inertial properties of the human body (AMRL Technical Report 74-137). Wright-Patterson Air Force Base, OH: Aerospace Medical Research Laboratories.

2.    Clauser CE, McConville JT, & Young JW (1969). Weight, volume, and center of mass of segments of the human body (AMRL Technical Report 69-70). Wright-Patterson Air Force Base, OH: Aerospace Medical Research Laboratories.

3.    de Leva, P (1996). Adjustments to Zatsiorsky-Seluyanov's segment inertia parameters. Journal of Biomechanics, 29(9), 1223-1230.

4.    Dempster, WT (1955). Space requirements for the seated operator (WADC Technical Report 55-159). Wright-Patterson Air Force Base, OH: Wright Air Development Center.

5.    Zatsiorsky V & Seluyanov V (1983). The mass and inertia characteristics of the main segments of the human body. In H. Matsui & K. Kobayashi (Eds.), Biomechanics VIII-B (pp. 1152-1159). Champaign, IL: Human Kinetics.

6.    Zatsiorsky V & Seluyanov V (1985). Estimation of the mass and inertia characteristics of the human body by means of the best predictive regression equations. In DA Winter, RW Norman, RP Wells, KC Hayes & AE Patlaa (Eds.), Biomechanics IX-B (pp. 233-239). Champaign, IL: Human Kinetics.

7.    Zatsiorsky V, Seluyanov V, Chugunova L (1990). In vivo body segment inertial parameters determination using a gamma-scanner method. In N. Berme & A. Cappozzo (Eds.), Biomechanics of Human Movement: Applications in Rehabilitation, Sports and Ergonomics (pp. 186-202). Worthington, OH: Bertec Corp.

8.    Zatsiorsky VM, Seluyanov VN, & Chugunova LG (1991). Methods of determining mass-inertial characteristics of human body segments. In GG Chernyi & SA Regirer (Eds.), Contemporary Problems of Biomechanics (pp. 272-291). Moscow: Mir.