114
A one-dimensional Newton-Raphson algorithm was programmed to- find* the zeros of the function f defined in Eq. (9.49) with d3 = 0.2, a1 = 0.3, a2 = 1, a4-= 1.5. Once a value of 91 for which f(e1)=0 was found, the corresponding solution set was completed and checked for consistency by verifying that the solution set satisfies the expression for ty as obtained from Eq. (7.1). This simple test proved
effective in filtering out extraneous solutions for this particular experiment. A more involved consistency verification procedure may be required for different manipulators. However, Computing the complete forward
kinematics from Eq. (7.1) and verifying all pose elements constitutes a worst case condition.
Inverse Kinematic Solution Search Algorithm
The one-dimensional inverse kinematic method just described was programmed in pascal on a personal microcomputer. A simple search algorithm was then
implemented by selecting regularly spaced values of the initial estimate of 9, within the interval [0, 2r) with the problem pose
-0.760117 -0.641689 0.102262 -1.140175
0.133333 0 0.991071 0
P = (9.57).
-0.635959 0.766965 0.085558 0
0 0 0 1
..