DH Parameters

  There are a few rules to consider in choosing the coordinate system:

1. the -axis is in the direction of the joint axis
2. the -axis is parallel to the common normal:
   If there is no unique common normal (parallel axes), then (below) is a free parameter.
3. the -axis follows from the - and -axis by choosing it to be a right-handed coordinate system.

Once the coordinate frames are determined, inter-link transformations are uniquely described by the following four parameters:

• : angle about previous , from old to new
• : offset along previous to the common normal
• : length of the common normal (aka , but if using this notation, do not confuse with ). Assuming a revolute joint, this is the radius about previous .
• : angle about common normal, from old axis to new axis

 

"Standard" DH Parameters

Following the DH standard you must provide 4 numbers that define the orientation of the ith link with respect to the i-1th link. "Standard" DH convention assumes that the ith coordinate frame is at the i+1 joint. (joint 1 axes 0, joint 2 axes 1 ...)

1. (Link parameter)(alpha)The first number represents the angle (in radians) between z_i-1 and z_i about x_i.
2. (Link parameter)(a)The second number represents the length (in meters) along x_i of the common perpendicular between z_i-1 and z_i.
3. (Joint parameter)(theta)The third number represents the angle (in radians) between x_i-1 and x_i about z_i-1.
4. (Joint parameter)(d)The fourth number represents the distance (in meters) along axis z_i-1 between the origin of the i-1th coordinate frame and the point where the common perpendicular intersects axis z_i

"Modified" DH Parameters (also called Craig's convention)

Following the modified DH standard, you must provide 4 numbers that define the orientation of the ith link with respect to the i-1th link. Unlike the "standard" DH convention, the "modified" DH convention assumes that the ith coordinate frame is at the i joint. (joint 1 axes 1,joint 2 axes 2 ...)

1. (Link parameter)(alpha)The first number represents the angle (in radians) between z_i-1 and z_i about x_i-1.
2. (Link parameter)(a)The second number represents the length (in meters) along x_i-1 of the common perpendicular between z_i-1 and z_i.
3. (Joint parameter)(theta)The third number represents the angle (in radians) between x_i-1 and x_i about z_i.
4. (Joint parameter)(d)The fourth number represents the distance (in meters) between x_i-1 and x_i about z_i.
   
   
   _{Many people in robotics are actually unaware that there are two different conventions in use. An advantage of Craig’s convention is the proximal placement of the origin for a link. Also the rotation  θi is about  zi and the joint number is the same as the coordinate number, which seem more natural. Torque exerted about joint i is also at the same place as at link i’s coordinate system, to which inertial parameters such as center of mass are likely to be referenced. A disadvantage is that the transform mixes i−1 and i parameters. Both Craig’s convention and the standard DH convention are equally valid. The choice of one over the other is merely a matter of taste or habit.}

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