The model center of gravity (COG) acceleration represents the translational acceleration of the center of mass of the entire biomechanical model.

The COG describes the mass-weighted average position of all segment centers of mass in the model. As the segments move relative to one another during motion, the position of the model COG changes over time. The COG velocity describes the rate of change of this position vector, and the COG acceleration describes the rate of change of the COG velocity.

In biomechanics, the acceleration of the center of gravity is commonly used to describe changes in the overall translational motion of the body. The terms center of mass (COM) and center of gravity (COG) are typically used interchangeably. While individual body segments may undergo different accelerations, the acceleration of the center of gravity provides a single quantity that summarizes the net effect of all forces acting on the body as a whole [1].

Visual3D computes the COG acceleration using the Compute Model Based Data command with the MODEL_COG_ACCELERATION function. Because the COG is derived from the mass-weighted combination of segment centers of mass, the resulting acceleration reflects the mass-weighted combined acceleration of all segments included in the model.

For a full description of how the model center of gravity is defined, see the Model Center Of Gravity page.

The model COG acceleration represents the instantaneous translational velocity of the entire body. The components of this vector correspond to the axes of the resolution coordinate system, typically the laboratory coordinate system. These components describe the direction and magnitude of whole-body motion. Common biomechanical uses include: analyzing whole-body movement during gait, studying balance and stability, and examining energy exchange during locomotion. For example, during walking the acceleration of the center of mass changes throughout the gait cycle as the body transitions between support phases and responds to ground reaction forces.

The model COG acceleration is directly related to the model COG velocity. The acceleration signal is the time derivative of the model COG velocity, meaning that any changes in segment configuration that affect the motion of the model center of gravity will also influence the computed acceleration.

For a detailed explanation of how the model COG is computed from segment centers of mass and anthropometric parameters, see the Model Center Of Gravity page.

The acceleration of the model center of gravity is defined as the time derivative of the model COG velocity. Since the model center of gravity is a mass-weighted average of segment center of mass velocities, differentiating that expression yields the following equation:

As illustrated above, the model COM acceleration is the mass-weighted average of the accelerations of all segments centers of mass.

The model COG acceleration is computed by differentiating the model COG position with respect to time. The derivatives are calculated using finite difference calculus. Specifically, they are calculated using the central difference method depicted here to get the first derivative of the linear velocity or second derivative of the linear position.

Calculating the model COG acceleration is done completely in the Visual3D background with the 'Compute Model Based Data' command and the 'Model COG Acceleration' selected in the 'Model Based Item Properties' dropdown. The only prerequisite is that the model has already been built, if is 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 acceleration.

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

If using a treadmill, the 'Treadmill Data' checkbox of the dialog allows the user to account for the direction and speed of the treadmill's belt.

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

Depending on how the data is being used, accelerations might need be to be filtered. Reference the Signal Processing page.

Compute_Model_Based_Data
/RESULT_NAME=COG_ACC
/SUBJECT_TAG=ALL_SUBJECTS
/FUNCTION=MODEL_COG_ACCELERATION
/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
;

• Older Visual3D versions
  • The model COG acceleration model-based item was added in Visual3D v2024.10.1. If working with older CMZ files, it is necessary to Recalc before running the Compute Model Based Data command.

• Research Methods in Biomechanics [2]

There is also a model-based item for MODEL_COG_VELOCITY. Or return to LINK_MODEL_BASED items.

[1] “Center of Mass | Formula, Velocity & Acceleration - Video,” study.com. Accessed: Mar. 17, 2026. [Online]. Available: https://study.com/academy/lesson/video/calculating-the-velocity-of-the-center-of-mass.html

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