Forward Kinematics with Denavit–Hartenberg Parameters

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What is forward kinematics?

It calculates a robot end-effector’s position and orientation from specified joint parameters.

What is inverse kinematics?

It determines joint parameters that achieve a specified end-effector pose.

What is an end-effector?

The tool or terminal part of a robot chain that interacts with the environment.

What are the four Denavit–Hartenberg parameters?

$\theta_i$, $d_i$, $a_{i,i+1}$, and $\alpha_{i,i+1}$ describe joint- and link-axis operations.

What does a serial-chain transformation product give?

The end link’s pose relative to the base.

Quiz questions

1. In the Denavit–Hartenberg convention used here, which operations form a joint transformation?Answer: Translation along the joint $Z$-axis, followed by rotation about that axis.
2. In the Denavit–Hartenberg convention used here, which operations form a link transformation?Answer: Translation along the link $X$-axis, followed by rotation about that axis.
3. Which Denavit–Hartenberg parameter commonly varies for a revolute joint, and which commonly varies for a prismatic joint?Answer: $\theta_i$ for a revolute joint and $d_i$ for a prismatic joint.
4. In a homogeneous transformation matrix, what does the upper-left $3\times3$ block represent?Answer: The rotation component of the transformation.
5. In forward-kinematics animation, what does the animator specify to calculate the positions of connected model parts?Answer: The model’s position and orientation, together with its joint values.