Robot Arm Movement Calculator

Calculation Results

Ready for calculation

End-effector position—

Orientation—

Movement time—

Tool-path distance—

Reachability—

Position error—

Estimated peak torque—

Workspace reach—

Enter robot data and select Calculate Movement.

Robot Configuration

Robot preset

Robot type

Degrees of freedom

Length unit

Angle unit

Gravity

Denavit–Hartenberg and Joint Data

#	Name	Type	a	α	d	θ / start	Target	Min	Max	Max speed	Max accel.	Mass	Gear ratio	Efficiency %

For revolute joints, θ and target use angle units. For prismatic joints, d and target use length units.

Base and Tool Offsets

Base X

Base Y

Base Z

Base yaw

Tool X

Tool Y

Tool Z

Payload mass

Calculation and Movement Mode

Calculation mode

Trajectory

Motion profile

Target Pose

Target X

Target Y

Target Z

Target roll

Target pitch

Target yaw

Preferred solution

IK tolerance

Timing and Waypoints

Requested duration

Sampling interval

Waypoint dwell time

Speed scale %

Maximum jerk

Cartesian speed

Waypoints

Safety and Movement Constraints

Maximum Cartesian speed

Maximum tool acceleration

Floor Z

Minimum clearance

Torque safety factor

Joint friction factor

IK position weight

IK orientation weight

Enforce joint limits

Check singularity risk

Check basic self-collision

Check floor clearance

Synchronise joint motion

Smooth trajectory

Obstacle boxes

Obstacle checks use sampled link points and axis-aligned boxes.

Movement Visualisation

Data, Presets, and History

Upload joint CSV

Saved calculation

Formula Used

Each joint uses a homogeneous Denavit–Hartenberg transformation matrix. The matrices combine link rotation, translation, twist, and offset values.

The forward solution multiplies every joint matrix in sequence. The final matrix gives tool position and orientation directly.

Inverse kinematics uses damped least-squares numerical iteration. It reduces pose error while respecting configured joint limits.

Aᵢ = RotZ(θᵢ) · TransZ(dᵢ) · TransX(aᵢ) · RotX(αᵢ)
T₀ⁿ = Tbase · A₁ · A₂ · … · Aₙ · Ttool
Δq = Jᵀ · (J·Jᵀ + λ²I)⁻¹ · e

How to Use

Select a robot preset or create a custom serial arm. Enter each link’s DH values, limits, speed, acceleration, and mass.

Choose forward, inverse, point-to-point, Cartesian, or workspace mode. Then provide a target pose and motion profile.

Select Calculate Movement to generate results and charts. Review warnings before using values in real equipment.

Example Data

Joint	Type	a	α	d	θ	Target
Shoulder	Revolute	350 mm	0°	0 mm	20°	45°
Elbow	Revolute	280 mm	0°	0 mm	35°	75°
Tool	Fixed offset	0 mm	0°	80 mm	0°	—

Assumptions and Limitations

The calculator models serial links using standard DH conventions. Complex parallel mechanisms require a specialised model.

Torque calculations are engineering estimates based on gravity, payload, friction, and simplified link mass distribution. Dynamic coupling remains approximate.

Collision checks use sampled geometry and rectangular obstacles. Validate every trajectory using certified robot software before operation.

Frequently Asked Questions

What does forward kinematics calculate?

It calculates the tool pose from known joint positions and robot geometry.

How is inverse kinematics solved?

A damped least-squares numerical solver reduces position and orientation error iteratively.

Can the calculator model prismatic joints?

Yes. Select prismatic and enter travel values using the chosen length unit.

Does it detect unreachable targets?

Yes. It compares reach, solver error, and joint limits before reporting status.

Are torque results suitable for motor selection?

They provide preliminary estimates. Final motor selection needs detailed dynamic and thermal analysis.

What is a singularity warning?

It indicates reduced controllability where small tool motions may demand large joint changes.

Can I upload joint data?

Yes. Upload a CSV containing name, type, DH values, limits, and motion ratings.

Can trajectories be exported?

Yes. Export sampled time, joint positions, tool coordinates, speeds, and accelerations.

Does the page save calculations?

Yes. Saved configurations and recent results use your browser’s local storage.