The D-H model of representation is a simple way of modeling robot links and joints that can be used for any robot configuration.
We will have to assign a z-axis and an x-axis for each link. The D-H representation does not use the y-axis at all. Let L
k be the frame associated with link k.
1. Define Z Axis from All Joints
From the axis of joint k+1, define the z
k axis for link k.
If the joint is revolute, the z axis is in the direction of rotation as followed by the right hand rule for the rotations.
If the joint is prismatic, the z-axis for the joint is along the direction of the linear movement.
2. Define Origins
The intersection of the z
k and z
k-1 axes is selected as the origin of L
k .
If they do not intersect, use the intersection of z
k with a common normal between z
k and z
k-1.
There is always one line mutually perpendicular to any two skew lines, called common normal, which is the shortest distance between them.
3. Define X-axis
Assign x
k in the direction of the common normal between z
k and z
k-1.
If z-axes are intersecting, select x
k to be orthogonal to both z
k and z
k-1
(the direction of the cross-product of the two z-axes).
If z
k and z
k-1 are parallel, point x
k away from
z
k-1 colinear with the common normal of the previous joint.
4. Define Y-axis
Select y
k to form a right-handed orthonormal coordinate frame L
k.
5. Define the Four Kinematic Parameters
*θ
k is defined as the angle between x
k-1 and x
k
axes about the z
k-1 axis.
*d
k is the distance between x
k-1 and x
k axes along z
k-1 axis.
*a
k is the distance between z
k-1 and z
k axes
along x
k axis.
*α
k is the angle between z
k-1 and z
k axes about x
k axis.
6. Transferring Frame k-1 to Frame k
*Rotation of L
k-1 about the z
k-1 axis by θ
k will make x
k-1 and x
k
parallel to each other. This is true because the common normals a
k-1 and a
k are both perpendicular to z
k-1 axis.
*Translation of L
k-1 along z
k-1 axis a distance of d
k will make x
k-1 and x
k colinear.
*Translation of L
k-1 along x
k axis a distance of a
k will bring the origins of L
k-1 and L
k together.
*Rotation of L
k-1 about x
k axis by α
k will make z
k-1 and z
k axes parallel.
At this point, frames L
k-1 and L
k will be exactly the same.
For simulation, a nice free software called
Robotassist can be downloaded at www.kinematics.com
Ref:
Introduction to Robotics -Analysis, Control, Applications; Second Edition, Saeed Benjamin Niku
Fundamental of Robotics -Analysis & Control, Robert J. Schilling
