During operation, in order to give the Delta robot design an optimal trajectory, it is in need to conduct in-depth research of its singularity and workspace. So, a mathematical model Delta robot forward kinematics was established, based on robot kinematics mathematical model, the method of partial differential was adopted to establish the Jacobi matrix of the robot, based on Jacobian matrix, the existence of Delta robot kinematics singular configurations was analyzed. At the same time the influence Delta robot working space constraints was analyzed, such as the range of rotation of the motor, the ball joint rotation range, and etc. Matlab software was used and based on the robot forward kinematics mathematical models, solving the given platform actuators on the robot work space of threedimensional (3D) map. Results of singularity and spatial analysis of robot, designed for nonsingularity trajectories provide a theoretical basis.