DH-Parameters
See the slides.
A standard for placing frames on a robot.
Every joint can be describes as a combination of prismatic and revolute joints.
Prismatic joint: Pure translation in one axis Revolute joint: Pure rotation in one axis
Variables
These values are derived for every link. $i$ denotes the link index.
$a_{i-1}$: Link length, shortest distance between two joint axis. $\alpha_{i-1}$: Link twist, the angle between the axis around $a_{i-1}$. $d_{i}$: Link offset $\theta_{i}$: Joint angle, angle of connection to the next joint, around the joint axis.
Placing Frames (Modified Craig)
- The origin of frame $\set{i}$ is located where $a_{i}$ intersects joint axis $i$.
- The Z-axis of frame $\set{i}$ is coincident with joint axis $i$.
- The X-axis of frame $\set{i}$ points along $a_{i}$ in the direction from joint $i$ to joint $i + 1$.
- The Y-axis of frame $\set{i}$ follows in order to form a right-handed coordinate system.
Procedure
See slide:
- Identify the joint axes and consider them as infinite lines
- Identify the common perpendicular between them or the point of intersection
- Assign the origins, Z-axes and X-axes of frames $\set i$ according to frame convention.
- Assign the Y-axes of frames $\set i$ to yield right-handed co
- Assign frame $\set 0$ and frame $\set N$ according to convention.
- For each pair of frames $\set i$ and $\set{i+1}$, identify the four DH parameters:
$\alpha_i$ - The angle from $\hat{Z}i$ to $\hat{Z}{i+1}$ measured about $\hat{X}_i$ $a_i$ - The distance from $\hat{Z}i$ to $\hat{Z}{i+1}$ measured along $\hat{X}i$ $d_i$ - The distance from $\hat{X}{i-1}$ to $\hat{X}_i$ measured along $\hat{Z}i$ $d_i$ - The angle from $\hat{X}{i-1}$ to $\hat{X}_i$ measured about $\hat{Z}_i$