The model Center Of Gravity (COG) represents the center of mass of the entire biomechanical model.

The COG (also known as the center of mass) is the point where a motionless body, if supported at that point, will remain balanced. It is at this point on a rigid body, where the mass of the body can be considered to be concentrated for motion analyses. The motion of this point describes the overall translational motion of the body and is commonly used to analyze balance, stability and whole-body movement. This lessens the amount of information that needs to be recorded about the body. The body's shape and structure can be ignored and only its center of gravity needs to be quantified [1].

In Visual3D, the COG is computed from the position of each segment center of mass and the corresponding segment mass properties defined in the model. The center of gravity is calculated by first calculating the center of mass of each kinetic segment and then calculating the center of mass across all of the model's kinetic segments [2]. As the segments move relative to one another during motion, the location of the COG changes accordingly

The trajectory of the model center of gravity represents the overall translational motion of the body during movement. Common biomechanical applications include: analyzing whole-body balance, examining dynamic stability, evaluating jump performance, estimating mechanical work and energy of the body. For example, during walking or running, the vertical displacement of the COG reflects the exchange between kinetic and potential energy during gait.

The model COM is computed as the mass-weighted sum of the segment COM positions [3]. The center of mass of the model is computed using the following equation.

The position of the model center of gravity (COG) depends on the anthropometric parameters used to define each segment of the biomechanical model. These parameters describe the mass properties of each segment, including:

• Segment mass
• Center of mass location
• Moment of inertia

Visual3D defines these parameters using a combination of anthropometric models.

Segment mass fractions are based on the work of Dempster [4], who quantified the relative mass of human body segments using cadaver studies. These values provide estimates of the proportion of total body mass associated with each segment (e.g., thigh, shank, foot).

The geometric representation of segments in Visual3D is based largely on Hanavan’s anthropometric model [5]. In this approach, body segments are approximated using simple geometric primitives. Most segments are modeled as frusta of right circular cones, which allows their inertial properties to be estimated using known geometric relationships. Using these geometric approximations, regression equations are applied to estimate the center of mass location and moment of inertia for each segment. These parameters define the inertial characteristics of the segment relative to its local coordinate system. Hanavan's geometric model of the body is shown in the figure below.

The center of mass for each segment is computed based on the segment’s defined inertial properties. Visual3D provides default anthropometric values for segment inertia and center of mass location; however, these values can be modified by the user if alternative anthropometric models or regression equations are desired. Segments that are defined as kinematic-only (virtual) segments are excluded from the calculation of the model center of gravity because they do not represent physical mass.

The model center of gravity is then calculated as the mass-weighted average of the centers of mass of all physical segments included in the model.

Calculating the model COG is done completely in the Visual3D background with the 'Compute Model Based Data' command and the 'Model COG' selected in the 'Model Based Item Properties' dropdown. The only prerequisite is that the model has already been built, if it has not, reference Building a 6 DOF Model. The image below shows the 'Compute Model Based Data' window for the inputs required to calculate the whole body center of gravity.

To express the 'Model COG' in the laboratory coordinate system, choose the LAB segment as the resolution coordinate system.

The output of this command is a [X Y Z] vector with a length of the complete data waveform. The units are SI distance units.

Compute_Model_Based_Data
/RESULT_NAME=COG
/SUBJECT_TAG=ALL_SUBJECTS
/FUNCTION=MODEL_COG
/SEGMENT=
/REFERENCE_SEGMENT=
! /RESOLUTION_COORDINATE_SYSTEM=LAB
! /USE_CARDAN_SEQUENCE=FALSE
! /NORMALIZATION=FALSE
! /NORMALIZATION_METHOD=
! /NORMALIZATION_METRIC=
! /NEGATEX=FALSE
! /NEGATEY=FALSE
! /NEGATEZ=FALSE
! /AXIS1=X
! /AXIS2=Y
! /AXIS3=Z
! /INCLUDE_REMOTE_ANGULAR_MOMENTUM=FALSE
! /TREADMILL_DATA=FALSE
! /TREADMILL_DIRECTION=UNIT_VECTOR(0,1,0)
! /TREADMILL_SPEED=0.0
;

• Representativeness
  • The degree to which the center of mass of a model's segments agree with the center of mass of the participant being modelled will depend on how well the individual is represented. For example, if the model includes only segments from the lower extremity than the center of mass of the segments will deviate substantially from the center of mass of the individual.
• COM vs. COG
  • In biomechanics, the terms center of mass (COM) and center of gravity (COG) are typically used interchangeably because gravitational acceleration is assumed to be uniform over the body.
• COG outside the body
  • It is possible to have the COG outside the human body when jumping or holding extreme postures. This does not mean your model has been incorrectly defined.

• Research Methods in Biomechanics, Chapter 3 [1].
• Thorough explanation of center of mass related specifically to biomechanics: https://biomechanist.net/center-of-mass/

In addition to 'Model Center of Gravity', there are also model based items for MODEL_COG_VELOCITY and MODEL_COG_ACCELERATION.

[1] D. G. E. Robertson, Ed., Research methods in biomechanics, Second edition. in Human Kinetics LIbrary. Champaign, IL: Human Kinetics, 2014. doi: 10.5040/9781492595809.

[2] “Center of mass,” Wikipedia. Feb. 17, 2026. Accessed: Mar. 12, 2026. [Online]. Available: https://en.wikipedia.org/w/index.php?title=Center_of_mass&oldid=1338856205

[3] “Kinematic Center of Mass: explanation of the code — Center of Mass v1.0 documentation.” Accessed: Mar. 12, 2026. [Online]. Available: https://center-of-mass.readthedocs.io/en/latest/kinematic_CenterOfMass_explanation.html?utm_source=chatgpt.com

[4] W. T. (Wilfrid T. Dempster, “Space requirements of the seated operator : geometrical, kinematic, and mechanical aspects of the body, with special reference to the limbs,” 1955, Accessed: Mar. 12, 2026. [Online]. Available: https://hdl.handle.net/2027.42/4540

[5] E. P. Hanavan, “A mathematical model of the human body.: (400822004-001).” 1965. doi: 10.1037/e400822004-001.