This paper presents a type of motion primitives that can be used for building efficient kinodynamic motion planners. The primitives are pre-computed to meet two objective: to capture the mobility constraints of the robot as well as possible and to establish a state sampling policy that is conductive to efficient search. The first objective allows encoding mobility constraints into primitives, thereby enabling fast unconstrained search to produce feasible solutions. The second objective enables high quality (lattice) sampling of state space, further speeding up exploration during search. We further discuss several novel results enabled by using such motion primitives for kinodynamic planning, including incremental search, efficient bi-directional search and incremental sampling.