Mechatronics & Automation

Robotics integrates MEC (mechanical engineering), EE (electrical engineering), and CS (computer science) into systems that sense, decide, and act in the physical world. This pack covers the core subsystems, control theory, and practical design patterns for robotic systems.

Robot Kinematics

KIN (kinematics) describes robot motion without considering forces. A robot manipulator is a kinematic chain of rigid links connected by joints. Revolute joints (R) provide rotational DOF (degrees of freedom); prismatic joints (P) provide linear DOF. A 6-DOF manipulator can reach any position and orientation in its WS (workspace) — the reachable volume.

FK (forward kinematics) computes end-effector position and orientation given joint angles. DH (Denavit-Hartenberg) convention assigns coordinate frames to each link using four parameters: link length (a), link twist (alpha), link offset (d), joint angle (theta). The homogeneous transformation matrix for each joint multiplies sequentially: T_0n = T_01 * T_12 * ... * T_(n-1)n.

IK (inverse kinematics) solves the reverse problem: given desired end-effector pose, find joint angles. IK is generally harder than FK — may have multiple solutions, no solution (outside WS), or singularities. Analytical IK (closed-form) is preferred when possible (6R with spherical wrist). Numerical IK uses iterative methods: Jacobian transpose, Jacobian pseudo-inverse, or damped least squares (DLS) to handle singularity-adjacent configurations.

The Jacobian matrix J maps joint velocities to end-effector velocities: v = J * dq/dt. At singularities, J loses rank — the manipulator cannot move in certain Cartesian directions regardless of joint velocities. Singularity avoidance or singularity-robust control is essential for smooth operation.