The work aims to study the number of branches of Delta parallel mechanism and the influence of driven joint distribution on the kinematic constraints of mechanism. Study parameters were used to represent the displacement and attitude transformation matrix of a rigid body. According to the D-H parameters of kinematic chain, constraint equations of kinematic chain were established, and then the branch constraint equations through coordinate transformation were obtained. The effect of driven joint distribution on the kinematic constraints of Delta parallel mechanism was analyzed. When the branch number was 3 and 4, no matter how the driven joint was distributed, the delta parallel mechanism was only characterized by movement. The unified expression used to indicate the constraining conditions of Delta parallel mechanism is more intuitive, and provides a new idea for its optimized design.