Question 1

What do α, a, d, and θ in Denavit-Hartenberg parameters each mean?

Accepted Answer

DH parameters consist of four values: α_{i-1} is the twist angle between z-axes along link i-1; a_{i-1} is the link length (shortest distance between z-axes); d_i is the joint offset (distance between x-axes); and θ_i is the rotation joint angle (twist angle between x-axes). These four parameters are used to construct a 4×4 homogeneous transformation matrix, and their sequential product yields the end-effector position and orientation.

Question 2

What is the difference between DH parameters for a PUMA robot and a SCARA robot?

Accepted Answer

The PUMA 6-DOF has all revolute joints, enabling spatial motion. Its α parameters take values of ±90°. The SCARA robot has 4 degrees of freedom: the first 3 joints rotate about vertical axes and 1 joint is a prismatic (linear) joint. SCARA uses mostly α=0° and specializes in horizontal plane motion, commonly used for high-speed assembly of semiconductor and electronic components. The UR robot is similar to PUMA but has a simpler structure where all α values are 0° or ±90°.

Question 3

What is the difference between forward kinematics and inverse kinematics?

Accepted Answer

Forward Kinematics (FK) solves for the end-effector position and orientation given the joint angles. The product of DH-parameter homogeneous transformation matrices yields a unique solution. Inverse Kinematics (IK) solves for joint angles given the desired end-effector position and orientation, requiring either an analytical solution or iterative numerical methods. Multiple solutions generally exist, and analytical solutions are only available for robots with specific geometries.

Question 4

How are DH parameters used in CAE simulation?

Accepted Answer

DH parameters are widely used in CAE simulation for robots: (1) Structural analysis — setting load boundary conditions for each link; (2) Dynamics simulation — defining joints in multibody dynamics codes (e.g., Adams, Simpack); (3) Collision detection — geometric representation of exact arm poses; (4) Control system design — building plant models for model-based control (MBD). ROS URDF format can also be generated from DH parameters.

Denavit-Hartenberg Parameters & Forward Kinematics Calculator

DH Homogeneous Transformation Matrix