Awakening Elementary School System in University

He liked dealing with people who were so straightforward.

He nodded and shot a look at Luo Qin beside him.

Luo Qin understood immediately. He opened his laptop, adjusted the angle, and pushed it to the center of the table.

Meanwhile, Fan Jianjun, who had been mostly quiet, cleared his throat. A sudden light sparked in his bright eyes.

He looked at Chen Lin and began to speak in a deep voice, personally laying out the core bottleneck Era of Creation was facing with its industrial software, explaining it to Chen Lin in mathematical terms.

"President Chen, the situation is this."

Fan Jianjun’s voice wasn’t loud, but his articulation was clear and his logic was rigorous. Every word conveyed a deep professionalism.

"In high-end CNC machining, especially when using five-axis linkage to machine complex surfaces, the toolpath must satisfy two conditions to achieve both efficiency and quality. First, it must be perfectly smooth. Second, it must never exceed the machine’s own kinematic limits."

He held up two fingers. "But that’s precisely where the problem lies. The raw path we export from CAD software is essentially a series of discrete points. The path connecting these points is often not smooth at the corners, leading to abrupt changes in acceleration.

"If the machine actually tried to follow that path, the intense vibration and shock would instantly destroy the expensive cutting tool, or even the spindle."

"Therefore, on the software side, we have to ’smooth’ this raw path. We need to generate a new, smooth trajectory that is at least C2 continuous, meaning position, velocity, and acceleration are all continuous."

"But that’s not all." Fan Jianjun’s expression grew even more serious. "A smooth trajectory alone isn’t enough. We also have to plan how the tool ’travels’ along that path. This is what’s known as ’velocity profiling’."

"Because the machine’s velocity, acceleration, and even its jerk all have physical upper limits. You can’t just have it accelerate from a dead stop to ten thousand RPM in 0.1 seconds—it’s not physically possible."

At this, he heaved a long sigh, his tone filled with frustration and reluctance. "And this... this is precisely where the biggest gap lies between us and Ximengzi from Hans Country. Their NX software can perfectly integrate both trajectory smoothing and kinematic constraints into a single optimization framework. The resulting paths are both fast and stable."

"Our software, on the other hand, either sacrifices speed to guarantee quality, or we chase speed and our yield rates suffer. We can never seem to get the best of both worlds."

Luo Qin had already pulled up a prepared presentation on the laptop, displaying clear diagrams and formulas that visualized the very problems Fan Jianjun was describing.

Finally, Fan Jianjun’s gaze locked onto Chen Lin. He slowly and deliberately stated the true purpose of their visit—the core problem that had plagued his entire team for years.

"So, we’re hoping you, President Chen, can help us design a mathematical optimization framework."

"Given an initial toolpath defined by N discrete points, along with the maximum allowable velocity (V_max), acceleration (A_max), and jerk (J_max) for each machine axis..."

"Your task is to generate a new, smooth toolpath that satisfies three strict constraints—geometric precision, C2 smoothness, and kinematic limits—and to determine an optimal motion profile that ultimately achieves one of two goals: either minimizing the total machining time or minimizing the shock to the machine."

"We need you to lay out the entire optimization framework. Specifically, you would need to explain: How do you parameterize the smooth path and the motion profile? How do you convert the discrete geometric constraints and the highly non-linear kinematic constraints into a set of unified constraints on the path and motion parameters? And finally, for this optimization problem, what are the optimization variables, the objective function, and the constraints?"

When he finished speaking, the office fell silent.