Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For K-12 Students · Motion Profile Generator

Motion Profile Generator for a CNC toolpath

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a CNC toolpath live below — adjust the inputs and watch it respond, right in your browser.

Forward Kinematics

open full solver →

Forward KinematicsLive

joint angles → end effector

Controls

Presets

Joint 1 angle (°)

Joint 2 angle (°)

Joint 3 angle (°)

Forward kinematics computes where a robot arm's tip ends up from its joint angles. Each link rotates relative to the previous one, so the transforms chain together. It is fast and unique — every set of angles gives exactly one end-effector position — which is why controllers use it constantly.

▶ Run in Python

Data Inspector

End X172.2

End Y110.4

Reach204.6

Links3

Governing equation

x = i \sum L_{i} cos (j \leq i \sum θ_{j}) = 172.2, y = i \sum L_{i} sin (j \leq i \sum θ_{j}) = 110.4

Reading this result: Reach 205 sits near the 210 maximum: the three links are nearly collinear, so the arm is almost fully extended.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

DC Motor

open full solver →

DC MotorLive

step response & speed-torque

Controls

Presets

Voltage (V)

Armature resistance (Ω)

Load torque (N·m)

Motor constant Kt (N·m/A)

A DC motor speeds up until back-EMF balances the applied voltage, giving a first-order step response. Its steady speed drops linearly with load along the speed-torque line: maximum speed at no load, maximum (stall) torque at zero speed. The green dot is the operating point where motor and load torque match.

▶ Run in Python

Data Inspector

No-load speed240 rad/s

Steady speed224 rad/s

Stall torque0.30 N·m

Current draw0.4 A

Reading this result: Light load: speed stays close to the no-load value, since only a small back-EMF drop is needed to supply the torque.

Governing equation

ω = \frac{V - I R}{k _{e}} = \frac{12 - 0.4 \cdot 2}{0.05} = 224 rad/s, τ = k_{t} I = 0.020 N\cdotm

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Motion Profile Generator for a CNC toolpath" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.