Denavit-Hartenberg convention for systematically describing robot manipulator kinematics using 4 parameters per joint. Overview Denavit-Hartenberg (DH) parameters provide a standardized way to describe the kinematic chain of a robot manipulator using only 4 parameters per joint. Purpose: Systematic representation of …

Practical examples of DH parameter configurations for common robot manipulators with complete Python implementations. 2-Link Planar Arm Simplest manipulator for learning DH parameters. Interactive 2-Link Arm DH Table Joint $\theta$ $d$ $a$ $\alpha$ 1 $\theta_1$ 0 $L_1$ 0 2 $\theta_2$ 0 $L_2$ 0 Implementation 1import …

Forward and inverse kinematics for four-wheel independent drive robots with individual motor control. Overview Four-Wheel Independent Drive uses four independently driven wheels, providing high maneuverability and redundancy. Advantages: High traction and power Redundancy (can operate with one wheel failure) Good for …

Forward and inverse kinematics for front-wheel drive robots with Ackermann steering geometry. Overview Front-Wheel Drive (FWD) combines steering and driving at the front wheels, similar to most cars. Advantages: Car-like steering (intuitive) Good forward traction Simpler than four-wheel steering Predictable handling …

Jacobian matrices relate joint velocities to end-effector velocities, essential for inverse kinematics and control. Overview The Jacobian matrix $J$ maps joint velocities $\dot{q}$ to end-effector velocity $\dot{x}$: $$ \dot{x} = J(q) \dot{q} $$ Where: $\dot{x} = [\dot{x}, \dot{y}, \dot{z}, \omega_x, \omega_y, …

Forward and inverse kinematics for mecanum wheel robots, enabling omnidirectional motion including sideways movement. Overview Mecanum wheels have rollers at 45° to the wheel axis, allowing omnidirectional movement without changing orientation. Advantages: Omnidirectional motion (can move in any direction) Can …

Forward and inverse kinematics for rear-wheel drive robots with front-wheel steering. Overview Rear-Wheel Drive (RWD) has driven wheels at the rear and steered wheels at the front, like many trucks and sports cars. Advantages: Better weight distribution Good for pushing/towing Better acceleration (weight transfer) …

Kinematics and control for two-wheel self-balancing robots (inverted pendulum on wheels). Overview A two-wheel balancing robot is an underactuated system that must continuously balance while moving, similar to a Segway. Key Characteristics: Inverted pendulum dynamics Inherently unstable (requires active control) 2 …

Forward and inverse kinematics for two-wheel differential drive robots, the most common mobile robot configuration. Overview Differential drive uses two independently driven wheels on a common axis with a passive caster or ball for balance. Advantages: Simple mechanical design Easy to control Can rotate in place (zero …