3D Transformation & Frame Visualization (Robotics)

MATLAB implementation of fundamental 3D transformation concepts used in robotics and kinematics.

This project builds step-by-step understanding of:

• Rotation matrices
• Homogeneous transformations
• Frame visualization
• Transformation composition

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Project Structure

3D-Transformation-Robotics

day1_rotation.m
day2_transformation.m
day3_composition.m
day4_2DOF_arm.m day5_Robot Arm Animation day6_Robot Arm Workspace

functions
rotZ.m
createTransform.m
drawFrame.m

images
day1_rotation.png
day2_transformation.png
day3_composition.png
day4_robot_arm.png day5_robotarmautomation.png day6_workspace.png

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Day 1 – Rotation Matrices

Implemented

• Rotation about Z-axis
• Orthogonality check (R * Rᵀ = I)
• Determinant verification (det(R) = 1)
• 3D vector rotation visualization

Mathematical Concept

A valid rotation matrix must satisfy:

RᵀR = I
det(R) = 1

Key Insight

A rotation matrix must be orthogonal and have determinant equal to 1.

Preview

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Day 2 – Homogeneous Transformation

Implemented

• Built 4×4 homogeneous transformation matrix
• Combined rotation and translation
• Transformed points between frames
• Visualized Frame A and Frame B

Mathematical Formulation

Homogeneous transformation:

T = [ R p
0 1 ]

Where:

• R is the rotation matrix
• p is the translation vector

Key Insight

Rotation and translation can be unified into a single matrix using homogeneous coordinates.

Preview

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Day 3 – Transformation Composition & Modular Design

Implemented

• Modular reusable functions (rotZ, createTransform, drawFrame)
• Transformation composition
• Visual comparison of multiplication order
• Structured project into reusable components

Concept Demonstrated

T₁ = R × Trans
T₂ = Trans × R

Transformation order changes the final pose.

Key Insight

Transformation composition order determines whether motion occurs in the global frame or the local frame.

Preview

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Day 4 – 2DOF Robot Arm (Forward Kinematics)

Implemented

• 2DOF planar robot arm
• Forward kinematics using transformation matrices
• Visualization of robot links and joints
• End-effector position extraction

Concept Demonstrated

x = L1 cos(θ1) + L2 cos(θ1 + θ2) y = L1 sin(θ1) + L2 sin(θ1 + θ2)

Forward kinematics computes the end-effector position from joint angles.

Preview

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Day 5 – Robot Arm Animation

Implemented

• Animated 2DOF robot arm
• Continuous joint motion
• Dynamic frame visualization

Concept

Robot motion can be simulated by varying joint angles over time.

Preview

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Day 6 – Robot Arm Workspace

Implemented

• Computed reachable workspace
• Sampled joint angles
• Visualized reachable points

Concept

Robot workspace represents all positions the end effector can reach.

Preview

Tools Used

• MATLAB
• Linear Algebra
• 3D Visualization

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Learning Roadmap

This project is part of a structured robotics learning path progressing toward:

• Forward Kinematics
• Denavit–Hartenberg Parameters
• Jacobian Analysis
• Robot Arm Simulation