Grasp planning for multifingered robotic hand is still time consuming. The crucial part is to find the contact points with collision detection techniques to evaluate the grasp quality and to guarantee that the hand does not collide with other objects. Our methods to accelerate the collision detection for grasp planning are presented in this paper. Grasping is performed in two steps: hand moving and finger closing. Finger links are a-priori known for both steps. We use precomputed bounding boxes to bound the extent of the finger links' motion to cull the objects that are far from robotic hand. A state-of-the-art continuous collision detection with conservative advancement is integrated to detect collisions between moving robotic hand and objects. For pick-and-place operation the environments by grasping and by placing are merged to one environment for grasp planning to find collision-free grasps for both pick and place. Ray intersections are further used to find out hidden grasping directions. We have tested our approach with three experiments: grasping a standalone object with one hand, two hands and grasping in complex environment. Results with four-fingered SAHands in simulation show the efficiency of the introduced methods.