The present paper deals with the dextrous workspace of a manipulator. A method is presented, for the first time, for analysing the dextrous workspace of practical manipulator with limited motion joints. A series of criteria are put forward, with which whether the dextrous workspace of a manipulator is existent can be deduced. At the end of the paper, an example of analysing the dextrous workspace is offered. As the analytical approach makes it possible to obtain the boundary surfaces of a dextrous workspace, it has the advantages of quickness and preciseness in calculation.