In the Denavit-Hartenberg convention, what four parameters describe the relation between adjacent links for a serial manipulator?

• A. A single parameter describes the whole chain; the others are constants.
• B. The four parameters are a_i, beta_i, gamma_i, delta_i.
• C. Each link i has four parameters (a_i, alpha_i, d_i, theta_i); the overall transformation is the product of individual link transforms.
• D. DH uses three parameters per link: a_i, alpha_i, d_i.

Answer: (C)

In the Denavit-Hartenberg convention you describe the relation between adjacent links with four parameters per link, and the overall pose of the end-effector comes from multiplying the per-link transforms along the chain. For each link i, the four parameters are a_i, alpha_i, d_i, and theta_i. These define the rigid transform from the frame on link i−1 to the frame on link i: a_i is the distance along the previous x-axis to the next z-axis, alpha_i is the twist angle between the previous and next z-axes about that x-axis, d_i is the distance along the new z-axis to the common normal, and theta_i is the rotation about the new z-axis from x_{i−1} to x_i. The resulting transform for link i is Generally written as A_i = RotZ(theta_i) TransZ(d_i) TransX(a_i) RotX(alpha_i). The overall transformation from the base to the end-effector is the product A_1 A_2 … A_n. The statement that each link carries four parameters and that the chain’s pose is the product of the per-link transforms captures the standard DH description. The other options either imply too few parameters, use nonstandard parameter names, or misstate how the chain is composed.