This paper presents the design strategy of serial manipulators with constraint satisfaction. The algorithm provides certified solutions to the range of values of the manipulator design parameters that satisfy the given constraints for all points inside a desired workspace. Alternatively, it can also be used to obtain the achievable workspace of a particular manipulator topology within which a set of given constraints are satisfied. This strategy can therefore be applied to the general case of a serial manipulator design problem, robots of adjustable parameters, or even reconfigurable robot strategy to obtain a suitable topology. The interval-based algorithm was implemented on an example serial anthropomorphic manipulator with joint displacement constraints and obtains the possible variations to the manipulator topology that allow the required workspace to be achievable under the given joint displacement constraints. Results are presented and discussed.