In this study, highly practical and reliable methods are proposed to determine arm solutions for a six-link robot manipulator. Based on a typical mathematical structure of minimizing an objective function, the optimization theory is applied to solve a reduced system of kinematic equations. The performance tests show that three different approaches are superior to a conventional method and of sufficiently practical use. Especially, the use of an algorithm presented in a linear search is promising.

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.

The familiar problem of maximizing the probability of choosing the best from a group of N candidates, where N is known, is extended to the case of N unknown. An a priori distribution is assumed for N, and the case of a uniform distribution is examined. Let VN denote the probability of choosing the best from a group of at most N candidates, then it is shown that limN→∞VN = 2e–2.