Delta Mechanics — Sports Biomechanics Lab

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Muscles glow brighter as the load they carry rises (illustrative, driven by the ground-reaction force on each leg).

Body mass — 70 kg External load (squat bar) — 60 kg

How an athlete makes load, speed & distance

Mass kg

70kg

profile + implement

Length m

pixels × S_cal

Time s

ΔN ÷ FPS

Test score

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Loadkg·m·s⁻²

Speedm·s⁻¹

0m/s

Distancem

Dimensional ladder — live

Every output is built from kg, m and s by multiplying or dividing one dimension at a time.

Parameter graphs

One smooth curve per parameter across the whole movement, inside its benchmark band: the dashed green lines are the upper and lower expected values (±10%). The marker follows the athlete; values change with body mass and external load.

[kg] Mass · kilogram

How much matter is moved. Entered in the athlete profile, plus any bar or implement. Split across body segments with Dempster's ratios to find the centre of mass.

[m] Length · metre

How far a landmark travels. The camera only sees pixels, so a known reference converts them: S = L_real / L_px in m/px.

[s] Time · second

How long it takes. Counted from frames: Δt = ΔN / FPS, or read directly from each frame's presentation timestamp.

Biomechanical quantities

Tap a row to inspect its dimensions.

Metric	Symbol	kg·m·s	SI	Formula

Dimension builder

Set the exponents of kg^a m^b s^c and see which quantity you have built.

You built

Buckingham Π — fair comparison

Dimensionless groups cancel kg, m and s so athletes of different size can be compared.

v (m/s)Leg L (m)Mass (kg) F peak (N)Power (W)

Fitness parameters and their units

Each field test reduces to one base quantity, which the camera measures from landmarks, calibration and frame times.

Parameter	Test	What is scored	Unit	kg·m·s	How computer vision measures it

Dimensional integrity check

Each formula used by the physics engine is verified by exponent arithmetic: multiplying adds exponents, dividing subtracts them.

From pixels to newtons

Five deterministic stages turn a video into calibrated mechanics. Each one grounds a base dimension or derives a new one.

Capture s

Video or live camera. Every frame carries a timestamp, which is the clock for all derivatives.

Δt = t[n] − t[n−1]

Calibrate m

Two points on a known length, or the athlete's stature, give metres per pixel.

S = L_real / √(Δx² + Δy²)

Pose

MediaPipe Pose Landmarker finds 33 body keypoints in the image and in 3D metric space.

33 × (x, y, z, visibility)

CoM + filter kg

Segment masses locate the whole-body centre of mass; a Butterworth low-pass removes jitter before differentiating.

CoM = Σ mᵢ·rᵢ / Σ mᵢ

kg·m·s physics

Differentiate twice, multiply by mass, and the load vector appears in newtons.

F = m·(a + g)

Local coordinate system

The origin sits on the athlete's centre of mass and travels with them.

X · red — along the ground in the image plane (direction of travel when filmed side-on)
Y · green — vertical, up, opposite to gravity
Z · blue — out of the image towards the camera (medio-lateral)

The frame is right-handed: X × Y = Z.

F = (Fx, Fy, Fz) = m·(ax, ay + g, az) · |F| = √(Fx² + Fy² + Fz²) newtons Direction: α = cos⁻¹(Fx/|F|), β = cos⁻¹(Fy/|F|), γ = cos⁻¹(Fz/|F|) — angles to X, Y, Z

Dempster segment masses

Segment	% body mass	CoM along segment

Joint motion

Each joint angle θ comes from the 3D landmarks either side of it. Angle is dimensionless kg⁰·m⁰·s⁰; angular velocity ω = Δθ/Δt is s⁻¹. Range of motion is θ_max − θ_min.

Camera → Record captures a real clip and analyses it. Video analyses an uploaded file. The simulated athlete needs no camera.

Additional camera views — optional

The main video is the side view (X, Y). Add any of these to measure what it cannot see: a front or top camera gives true sideways motion Z. Tick a view to use it. With the simulated athlete the views are generated; with an uploaded main video, load one video per view filmed at the same time.

Athlete profile & calibration

Body mass kg Ext. load kg Stature m Leg length m Benchmark level % Filter cut-off Hz Pose model Ref. length m Scale

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Test score

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Pick a test, then simulate, record or upload.

Benchmark check● OK● >10%● >25%

Measured values are compared with the expected curve for this test.

Load |F|kg·m·s⁻²

—N

Fx — · Fy — · Fz — N

direction —

Speedm·s⁻¹

—m/s

—

a —

Distancem

—m

—

Phases

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Powerkg·m²·s⁻³

—W

Workkg·m²·s⁻²

—J

Impulsekg·m·s⁻¹

—N·s

Π₁ Froude

—

v²/(g·L)

Π₂ Rel. load

—

F_peak/(m·g)

Π₃ Power idx

—

P/(m·g³ᐟ²·L¹ᐟ²)

Force – time (N)Fx Fy Fz |F| ▒ expected

Velocity – time (m/s)

Displacement – time (m)X Y

Force – velocity profile|F| vs |v|

Acceleration – time (m/s²)

Power – time (W)

Work – time (J)cumulative

Joint motion analysis

3D joint angles from MediaPipe world landmarks. Tap a joint to chart it. 180° = fully extended. Deviation compares each angle with the expected posture at the same point of the movement.

Joint	θ (°)	ω (°/s)	ROM (°)	min – max		Expected (°)	Deviation

Knee R — angle (°)θ · ω/10

PDF report

Athlete name Movement / test

Change logo…

XIFT logo header, athlete details, annotated snapshot, results table, every chart with its expected band, a benchmark check with images of the frames that need correction, the joint-motion table, and XIFT's address and contact on the last page.

Export

Live values use a causal 4th-order Butterworth filter. "Zero-lag recompute" re-filters the recording forwards and backwards for report-grade numbers.