In order to calculate the workspace of Delta parallel manipulators under mechanical constraint fast and conveniently, a new numerical method to calculate the workspace of Delta parallel manipulators is proposed. In this method, the influence of some mechanical constraints such as ball joints, universal joints to the workspace of Delta parallel manipulator was considered.First, the theoretical mathematical model of computing the workspace of Delta parallel manipulators was derived; then the mathematical model of angular constraints of ball joints and universal joints were built; lastly, solving these models by MATLAB programming, mapping the calculation result by discrete points, and verifying the results through experiment. This calculation method can be used to calculate the workspace of Delta parallel manipulators under mechanical constraint. By operating experiment on the Delta parallel manipulator designed and manufactured independently, the validity of this method is verified.