did a bit hard Berg parameters allow you to succinctly describe the motion of a series of ridges joints this is useful for efficient calculation of forward and inverse kinematics the process begins by defining the z axis along the axis of rotation for our village joints or the axis of translation for prismatic joints since this is the first joint the x axis is a free choice for later joints each x axis will point away from the previous joint the y axis simply completes the right handed reference frame now if we add another joint we can determine the transformation between them as before the z axis points along the axis of rotation the d.h parameters will be derived from the common normal between these z axes the common normal is orthogonal to both vectors as also the shortest line between them the new x axis points along the common normal and has its origin at the intersection of the new z axis notice the origin is not within the physical actuator because the d-h perimeters are only concerned with the motion of the links not the physical placement of components using this protocol for laying out the reference frames only for parameters are needed the first of these d is the depth along the previous joint z axis from the origin to the common normal Theatre rotates about the previous z-axis to line the x-axis R is the length of the common normal itself most texts call this parameter a which is unfortunately easy to confuse with alpha instead calling it R is a useful dynamic as this is also the radius of revolution for the new origin about the previous Z finally alpha rotates about the new x-axis to bring Z into alignment with the axis of joint motion now there's one special case when the z axes are parallel because parallel lines have an infinite number of common normals you can choose any D value like in order to place the new origin at a convenient location such as the center of the link or the tip of an end effector the other parameters are the same as before theta rotates about C to align the x axis with the normal an R translates out along the normal to reach the new origin alpha is already known to be 0 in this case since the z axis must be parallel for this to apply thus no rotation is needed congratulations that's all there is to it you