Robotics

Robot kinematics relates joint variables to end-effector pose using Denavit-Hartenberg transformations. Forward kinematics gives pose from joints; inverse kinematics gives joints from pose, per robotics texts (Groover/Mittal).

Actuators (electric, hydraulic, pneumatic) drive robot joints; a DC motor gives torque τ = K_t·I. Sensors (encoders, force, vision) provide feedback for control, per robotics texts.

Trajectory planning generates smooth joint (or Cartesian) paths versus time; a cubic polynomial q(t) = a₀ + a₁t + a₂t² + a₃t³ meets position and velocity boundary conditions, per robotics texts.

Robots are programmed by teach-pendant (lead-through), offline (simulation), or textual languages; motion commands like MOVEJ (joint interpolated) and MOVEL (linear) define paths, per robotics texts.

Industrial robots perform material handling, welding, painting, assembly, and inspection; cycle time = Σ(motion time + process time) drives throughput. Application selection weighs payload, reach, accuracy, and speed, per robotics texts.