Delta Robot Kinematics Calculator & 3D Workspace Simulator

Professional 3D workspace simulator for parallel linkage robotics. Calculate inverse kinematics and forward kinematics for Delta robot configurations with real-time visualization.

📋 Share this Tool

How to Use This Calculator

1. Configure Robot Parameters: Enter your Delta robot's geometric specifications including base radius, bicep length (upper arm), and forearm length.
2. Input Target Coordinates: Specify the desired end-effector position in 3D space (X, Y, Z coordinates in mm).
3. Calculate Kinematics: The tool automatically computes joint angles using inverse kinematics equations for the parallel linkage mechanism.
4. Visualize Workspace: View the 3D representation of your Delta robot's reachable workspace and current configuration.
5. Export Results: Download calculated parameters and joint angles for use in your robotics control system.

Technical Reference

Understanding Delta Robot Geometry

A Delta robot is a type of parallel manipulator characterized by three arms connected to universal joints at the base. Each arm consists of two segments: a bicep (upper arm) attached to an actuated revolute joint, and a forearm (lower arm) connected via a parallelogram linkage. This unique configuration maintains the end-effector orientation parallel to the base throughout the workspace, enabling high-speed, precise motion with excellent rotational symmetry.

The geometry is defined by three critical dimensional parameters:

• Base Radius (r_b): Distance from the center to each actuated joint on the fixed base platform
• Bicep Length (L_1): Length of the upper arm segment from the actuated joint to the elbow
• Forearm Length (L_2): Length of the parallelogram linkage from elbow to end-effector connection

Inverse Kinematics vs. Forward Kinematics

Inverse Kinematics (IK) solves for the joint angles (θ₁, θ₂, θ₃) required to position the end-effector at a specified Cartesian coordinate (X, Y, Z). This is the most common calculation in robot control, as it translates desired tool positions into motor commands. For Delta robots, the IK solution involves solving three coupled geometric constraints derived from the sphere-sphere intersection of the forearm reach spaces.

Forward Kinematics (FK) determines the end-effector position given a set of joint angles. While computationally more complex for parallel linkage systems than serial manipulators, FK is essential for simulation, verification, and workspace analysis. The solution requires iterative numerical methods to resolve the intersection of three spherical surfaces.

Geometric Parameters: Base, Biceps, and Forearms

The workspace volume and reachability of a Delta robot are directly determined by the ratios between its geometric parameters:

• Base Radius: Larger base radius increases lateral workspace but reduces vertical reach depth
• Biceps Length: Affects the arm's reach envelope; typical ratios to forearm length range from 1:2 to 1:3
• Forearms Length: Primary determinant of overall reach; longer forearms extend workspace but may reduce stiffness
• End-Effector Radius: Smaller end-effector platform relative to base increases dexterity within the workspace

Understanding these relationships is crucial for optimal Delta robot design for specific applications, whether high-speed pick-and-place, 3D printing, or precision assembly tasks.

Workspace Point Cloud Visualization

The point cloud displayed in the 3D viewport represents the complete reachable workspace of your Delta robot configuration. Each point indicates a position where the end-effector can be positioned given the current geometric parameters (base radius, bicep length, and forearm length).

The point cloud is generated by systematically sampling valid end-effector positions throughout the robot's operational volume. This visualization helps engineers:

• Identify workspace boundaries: See the exact limits of where the robot can reach
• Evaluate workspace shape: Understand how the reachable volume changes with different parameters
• Plan tool paths: Ensure desired positions fall within the accessible workspace
• Optimize design: Visualize how parameter changes affect the working envelope

Configuration Comparison Feature

The comparison mode allows you to overlay two different robot configurations simultaneously, displaying both workspace point clouds in the same 3D view. This powerful feature enables direct visual comparison of how geometric parameter changes affect the workspace.

How to use comparison mode:

1. Configure your first robot design (Configuration A) with desired parameters
2. Enable comparison mode to create a second configuration (Configuration B)
3. Adjust parameters in Configuration B to explore alternative designs
4. Both workspace clouds are displayed with distinct colors for easy differentiation

Why use comparison mode:

• Design optimization: Quickly evaluate how increasing bicep or forearm length expands the workspace
• Trade-off analysis: Compare compact vs. extended reach configurations side-by-side
• Client presentations: Demonstrate workspace differences between proposed robot variants
• Constraint validation: Verify that parameter modifications maintain required reach zones