The Center of Gravity (COG) refers to the point where the mass of the entire body appears to be concentrated. In human movement — and especially in dance — understanding the location and behavior of the COG and it's relation to the Center Of Support (COS) is critical to mastering balance, poise, and the control of motion.

For example: Stand on one leg. The wobbly feeling you might feel is your brain trying to keep your COG over the standing foot (the COS).

🧠 Conceptual Overview

The human body is not a single rigid object; it's a collection of segments, each with its own shape, mass, and movement potential. To calculate the COG (Center Of Gravity), we must treat the body as a composite system of these segments. Each one contributes to the overall COG depending on:

• Its mass
• Its position in space
• The location of its own center of mass

The dancer’s COG is constantly shifting — even subtle changes in head position, arm styling, or foot placement can move the COG and influence balance. A well-controlled dancer doesn't just “stay upright”; they manage their COG with intention, especially during transitions, rotations, and moments of stillness.

Blocks of Weight

You've probably heard someone say "align your blocks of weight" and it's a term that has been with us for many, many decades. But... nobody ever seems to describe what your 'blocks of weight' are and how to align them. OK, ok there are mentions of head, chest etc., but nothing specific about what they contribute.

Welcome to the wonderful world of Body Segments

Body Segment Based COG

In our biomechanical model, the body is divided into labeled segments, each derived from anatomical standards. These are organized into key anatomical groups:

S1 – Head & Neck

• S1: Head_Neck

  S2 – Torso

• S2: Thorax
• S3: Abdomen
• S4: Pelvis_Center

  S2L – Left Arm

• S2LU: UpperArm_L
• S2LL: LowerArm_L
• S2LH: Hand_L

  S2R – Right Arm

• S2RU: UpperArm_R
• S2RL: LowerArm_R
• S2RH: Hand_R

  S5L – Free (Non-Supporting) Leg

• S5LU: FreeThigh
• S5LL: FreeCalf
• S5LF: FreeFoot

  S5R – Standing (Supporting) Leg

• S5RU: StandingThigh
• S5RL: StandingCalf
• S5RF: StandingFoot

Each of these segments has a known mass proportion and a center of mass location (usually a percentage along its length from the proximal end). By combining the positions of all segment centers of mass — weighted by their respective masses — we calculate the overall COG.

The Red X is an example of approximately where an average persons COG will be. This is an example only!

Why It Matters in Dance

Dancers often speak of “staying over their foot” or “maintaining balance,” but these are qualitative ways of describing COG control. In physics terms:

• If the COG is within the Center of Support COS) (e.g., the standing foot), balance is stable.
• If the COG moves outside the COS, balance must be recovered through motion, counterbalance, or muscular effort.

Understanding the COG pathway during figures — especially turning actions, foot passes, or moments of suspension — allows for better, smoother transitions, and reduced risk of overbalancing.

In short, the COG is not just an abstract physics concept — it's the literal heart of poise, grace, and grounded movement. Every great dancer uses it — even if they’ve never called it by name.

The Two Centers of Gravity in Dance

Although we speak of "the" center of gravity (COG), a dancer actually manages two interacting COGs at any moment during standing movement:

COG 1 – The Standing Leg

This COG is determined only by the supporting side of the body. Assuming the dancer is standing on their Right Foot:

• S5RU – Standing Thigh
• S5RL – Standing Calf
• S5RF – Standing Foot S5Rf is the Center of Support (COS)

This is the part of the dancer's body in direct contact with the floor. Its COG remains relatively fixed unless the knee flexes, the hip rotates, or the foot articulates (e.g., through pressure, rise, or foot rotation).

We refer to this as the primary base COG, or COG 1, because it defines the base of support. It acts like a foundation — everything else must balance around it.

COG 2 – The Rest of the Body

This is everything else:

• The torso, head, arms, and the non-standing leg
• All the upper body segments:
  • S1, S2, S3, S4
  • S2LU, S2LL, S2LH
  • S2RU, S2RL, S2RH
• And the free leg:
  • S5LU, S5LL, S5LF

This collection is in continuous motion — rising, lowering, swaying, reaching, counterbalancing. Its combined COG shifts constantly and dynamically in response to motion and styling.

We refer to this as COG 2, or the Active Mass COG — because it’s the one the dancer manipulates to maintain poise, create shaping, and control momentum.

🔢 The Relationship Between COG 1 and COG 2

To remain balanced:

• COG 2 must be coordinated in such a way that its influence passes through the support area defined by COG 1.
• If COG 2 shifts too far outside the zone of control (e.g., during a lunge or oversway), the dancer must compensate with muscular effort or transition to another figure.

When both COGs are aligned correctly, movement feels light, responsive, and under control.
When they are not — dancers feel “pulled off balance,” “heavy,” or “late.”

🧠 Summary

Think of COG 1 as the point you balance on, and COG 2 as the shape and energy you control.
The artistry of ballroom comes from moving COG 2 through space while keeping COG 1 stable — until it's time to transfer support and switch roles.

This dual-COG model is central to DanceBot's biomechanical system and underpins everything from sway analysis to poise zone classification.

If you are interested in how your COG is calculated (it's worth knowing) read on, otherwise you can skip to 👉 the Center Of Support

🧮 How to Calculate Each Center of Gravity

In our biomechanical system, we calculate each center of gravity (COG) using the mass-weighted average of the 3D positions of each body segment’s center of mass.

General Equation (applies to both COG 1 and COG 2):

Let:

• m_i = mass of segment i
• (x_i, y_i, z_i) = position of segment i’s center of mass
• M = total mass of the included segments (∑ m_i)

Then the overall center of gravity is given by:

\[ x_{cm} = \frac{\sum m_i x_i}{M} \\ y_{cm} = \frac{\sum m_i y_i}{M} \\ z_{cm} = \frac{\sum m_i z_i}{M}\]

How to Calculate Each Center of Gravity

This is computed independently for each axis (X, Y, Z) to produce the full 3D coordinate of the COG.

COG 1: Standing Leg and Foot

This includes only the support-side leg:

• S5RU: StandingThigh
• S5RL: StandingCalf
• S5RF: StandingFoot

Each segment’s mass and center position is used in the standard mass-weighted COG formula.

COG 2: Everything Else

This includes all other segments:

• Head, torso, arms, and free leg:
  • S1, S2, S3, S4
  • S2LU, S2LL, S2LH
  • S2RU, S2RL, S2RH
  • S5LU, S5LL, S5LF

The same formula applies, but with this broader set of segments.

Interpretation

These two centers (COG 1 and COG 2) give us a powerful model:

• COG 1 represents stability and ground connection.
• COG 2 represents motion and control of the upper structure.

DanceBot uses this model to analyze poise, sway, and torque, giving dancers a quantitative view of movement mechanics that are often described using only stylistic or aesthetic language.

📊 Where Do the Segment Masses (m_i) Come From?

The values for m_i — the mass of each body segment — are based on established anatomical research. These values are typically represented as a percentage of total body weight.

DanceBot uses these standardized values to ensure consistency in calculations. While the exact proportions vary slightly across studies, we use the most commonly accepted averages based on adult human anatomy.

🧍 Standard Segment Mass Percentages

📊 Segment COG and Mass Fractions (Male vs. Female)

These tables provide a comparison of segment mass fraction and Center of Gravity (COG) percentage from the proximal end for both male and female anatomical models, as used in DanceBot's biomechanical calculations.

🧠 Notes

• Mass % refers to the percentage of total body mass.
• COG % is the center of gravity location as a percentage of the segment length from the proximal (top/attached) end.
• The Pelvis's 'proximal' is from the point where it joins the spine.
• Some male-only segment definitions (like Pelvis_Center, S4L, S4R) are used for detailed pelvis articulation in 3D pose construction.
• Female segment definitions are slightly more streamlined but compatible.

🔬 Source of Data

These values are drawn from classical biomechanics literature, including:

• Dempster (1955) – Space Requirements of the Seated Operator
• Winter (2009) – Biomechanics and Motor Control of Human Movement
• Additional adjustments derived from contemporary gait and motion studies

🛠 How to Use These in Practice

You can do the math (which is fun!) or refer to the tables below:

COG Lookup Table for Men and Women

Estimated vertical Center of Gravity (COG) based on dancer height alone. Mass is not required for this table — COG height is proportional to height.

• On average, female dancers have a COG approximately 3–4 cm lower than males of the same height.
• This affects poise, sway response, and torque leverage during movement.
• Use this table to determine approximate COG height for static postures.
• Dynamic movements (sway, poise, leg extension) will shift this value.

And if you want to do the math yourself (because it's fun!)

To compute m_i for a dancer:

1. Determine their total body mass (e.g., 70kg)
2. Multiply by the segment’s mass fraction (e.g., 0.10 for a thigh)
3. Use the result as m_i in the COG formula

For example:

• A 70kg dancer’s thigh contributes:
  • m_i = 70kg × 0.10 = 7.0kg

Repeat for each segment and plug into the 3D COG equation.

Understanding these mass distributions helps DanceBot calculate how limb movements — even small ones — affect balance, torque, and control. It gives dancers an analytical insight into the very forces they feel every day.

👉 Next, the Center of Support