Applications of robots in tasks where the robots end-effector bears loads, such as manipulating or assembling an object, picking-and-placing loads, grinding or drilling, demand precision. One aspect that improves precision is the limitation, if not elimination, of manipulator compliance. This paper presents a manipulator compliance optimization approach for determining an optimal manipulator configuration for a given position in the robots task space. A numerical solution for minimal compliance, a nonlinear constrained optimization problem, is presented for an arbitrary position and illustrated by an example, using a model developed on ADAMS software and using MATLAB optimization tools. Also, this paper investigates the optimal value function for robot tasks in which the tool-point is subjected to applied force as it generates an important trajectory such as in grinding processes. The optimal value function is needed for optimal configuration control.