We present Flaticulation, a method to laser cut joints that clutch two cut-in-place flat boards at designated articulated angles. We discover special T-patterns added on the shared edge of two pieces allowing them to be clutched at a bending angle. We analyze the structure and propose a parametric model regarding the T-pattern under laser cutting to predict the joint articulated angle. We validate our proposed model by measuring real prototypes and conducting stress-strain analysis to understand their structural strength. Finally, we provide a user interface for our example applications, including fast assembling unfolded 3D polygonal models and adding detent mechanisms for functional objects such as a mouse and reconfigurable objects such as a headphone.