Motion planning is a critical issue in CAD/CAM manufacturing systems. Many interpolation algorithms based on velocity-based finite-impulse-response (FIR) filters have been proposed to interpolate fast and smooth trajectories, in which the reference trajectories are usually composed of a series of linear segments. Those methods, however, possess two main limitations: first, they can only interpolate trajectories that maintain the same target velocity, i.e., the corner error equations will fail if the target velocities are different around different corners. Second, many systems have different kinematic constraints around different corners, but all of the methods can only process fixed and conservative kinematic constraints. In order to overcome these two limitations, an interpolation algorithm based on acceleration-based FIR filters is proposed. By applying FIR filters to the acceleration base, the motion planning process will comprise several individual convolution processes. The filters and constraints in each convolution process can be designed differently. Therefore, the interpolation algorithm can generate trajectories with different target velocities and kinematic constraints because the taps and types of FIR filters can be changed accordingly during the interpolation process. The experiment results show that, by applying the proposed method to a non-linear kinematic system, more than 10% of motion time is saved when compared to a velocity-based method, the performance of the system can be fully utilized, and efficiency can be markedly improved.