## Sunday, March 23, 2014

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

1. the $z$-axis is in the direction of the joint axis
2. the $x$-axis is parallel to the common normal: $x_n = z_n \times z_{n - 1}$
If there is no unique common normal (parallel $z$ axes), then $d$ (below) is a free parameter.
3. the $y$-axis follows from the $x$- and $z$-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:
• $\theta\,$: angle about previous $z$, from old $x$ to new $x$
• $d\,$: offset along previous $z$ to the common normal
• $r\,$: length of the common normal (aka $a$, but if using this notation, do not confuse with $\alpha$). Assuming a revolute joint, this is the radius about previous $z$.
• $\alpha\,$: angle about common normal, from old $z$ axis to new $z$ 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 ...)
2. (Link parameter)(a)The second number represents the length (in meters) along xi of the common perpendicular between zi-1 and zi.
3. (Joint parameter)(theta)The third number represents the angle (in radians) between xi-1 and xi about zi-1.
4. (Joint parameter)(d)The fourth number represents the distance (in meters) along axis zi-1 between the origin of the i-1th coordinate frame and the point where the common perpendicular intersects axis zi

## "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 ...)