Robot Arm Movement Calculator

Enter Robot Arm Data

Example Data Table

Formula Used

This calculator uses two link planar inverse kinematics.

Reach: r = √(x² + y²)

Elbow angle: cos(θ₂) = (x² + y² − L₁² − L₂²) / (2L₁L₂)

Shoulder angle: θ₁ = atan2(y, x) − atan2(L₂ sin θ₂, L₁ + L₂ cos θ₂)

Angular speed: ω = |Δθ| / time

Acceleration estimate: α = 4|Δθ| / time²

Payload torque: T ≈ mass × gravity × horizontal arm distance × safety factor

How to Use This Calculator

1. Select the unit used by your drawing or robot layout.
2. Enter both link lengths using the same unit.
3. Enter the start and target tool coordinates.
4. Add payload, movement time, motor speed, gravity, and safety factor.
5. Select elbow up or elbow down to compare arm posture.
6. Click calculate and review the result above the form.
7. Download a CSV or PDF report for records.

Robot Arm Movement Planning

A robot arm calculator helps builders study movement before code reaches hardware. It turns link sizes, coordinates, load, and time into practical motion values. The result shows whether a point is reachable. It also shows the joint angles needed to place the tool tip. This early check can prevent stalled motors, wasted prints, and unsafe test runs.

Why Movement Geometry Matters

A two link arm moves through arcs, not straight rails. Each target point requires a shoulder angle and an elbow angle. Small coordinate changes can create large joint changes near the edge of the workspace. That is why reach, angle change, speed, and torque should be reviewed together. A reachable point can still be too fast or too heavy for the selected motors.

What This Calculator Measures

The tool uses planar inverse kinematics for a two segment arm. It accepts start coordinates and target coordinates. It then estimates start angles, target angles, joint travel, angular speed, angular acceleration, straight path distance, and payload torque. The elbow option lets you compare elbow up and elbow down movement. This is useful when a gripper must avoid a wall, bench, fixture, or product tray.

Using Results In Projects

Use the angle results as planning values for servos, steppers, or geared motors. Compare the required joint speed with your motor limit. Add a safety factor when payloads move quickly or stop suddenly. Torque estimates assume the load acts at the tool point. Real arms also need allowance for link weight, friction, gear losses, cable drag, and emergency stops.

Good Workflow

Start with realistic link lengths. Enter points that match your drawing scale. Choose the same unit for every coordinate and length. Use a longer move time when the required speed is too high. Test unloaded first, then add the payload gradually. Export a CSV or PDF report for build notes. Keep each report with the related robot version, motor choice, and controller settings.

Common Planning Checks

Check the reach warning first. Then compare speed, acceleration, and torque. If one value looks high, change the path or increase the move time. For repeat work, save each setup during careful testing. Clear records make later tuning faster and reduce setup mistakes.

FAQs