This paper is concerned with an efficient continuous variable optimization method for determining an optimal configuration of passive and active joints of a binary manipulator when it operates within a desired sub-workspace. When joints are passive, their states, either stretched or contracted, are also determined by the developed method. Manipulator operations in a sub-workspace can avoid unnecessary actuations, resulting in energy saving. A technique to increase the sub-workspace concentration degree for a given maximum number of allowable active joints is also suggested.