In this paper, the constrained motion control of a normally unconstrained mechanical system is investigated. As far as its motion control is concerned, such a system will have a redundancy in its actuators due to the reduction caused in its number of degrees of freedom by the presence of the constraints. Four methods are described in order to determine the actuator and constraint forces. The first three of these methods necessitate using all the actuators and the fourth method is applicable in a case where non-redundant (i.e. minimum) number of actuators is used. In such a case, it is shown that there exist actuation-related singular configurations (ASCs), at which the actuator and constraint forces become unboundedly large, unless some special precaution is taken. The fourth method includes an efficient precaution as well. As a case study, computer simulations are made considering a typical constrained system that consists of two cooperating manipulators. Only the fourth method is applied because it is preferable with its minimal operational complexity and also because its application needs extra care due to the troublesome but interesting phenomenon of ASCs.