One + One-half = Four

“Rick?” Becca burst into her colleagues office with her laptop half open. “In the 3D-Printer specification you state that the extruding-head must move precisely to four equally spaced positions.”

Rick let go of his mouse, leaned back and put his finger tips together. “Yah, that’s because there are four filament spools for four polymers. What’s the problem?”

Becca closed and clutched her warm laptop under one arm. “You said the production cost is limited to $50.00 each for the actuator sub-assembly and the electronics. That’s impossible, the stepper motor and driver electronics alone will take more than half that, even if we produce a million of them.”

Rick leaned forward, palms up. “The specification doesn’t require a stepper. Your requirement is to design the machine to move four print-head assemblies, including feed spools to one of four positions, three inches apart, to an accuracy of…”

“I know the resolution, 0.1 millimeters, and that’s going to require either a stepper with gear-head, or servo motor system.”

Rick raised an eye-brow and breathed deep.

“What else is there?” Becca leaned over Rick’s desk. “If there were only two spools, this would be easy, I could just use a solenoid or a pneumatic piston to make the tool change. Whether extended or retracted, the cylinder would stop precisely.”

“You’re trying to do this all by yourself aren’t you?” Becca lowered her shoulders and took a breath thinking, “I knew he’d say something like that. He’s always…”

“Did you consider using two cylinders?” Rick said. “What if you mounted two cylinders end-to-end?”

Becca placed a finger on her chin, lips pressed together, and turned her eyes toward the wall.

Rick leaned back in his chair.

“It wont’ work,” Becca concluded. That will give you three positions, not four.”

“Look, you need to play with some options here. Get together with another perspective, someone who thinks…”

“I know, I know. Someone who thinks a little different.”

Rick folded his arms.” Your too stiff, too binary in your thinking.”

Becca opened her mouth to speak, but nothing emerged. “Binary? What does he mean by that?” She moved her laptop to the other arm, turned, and walked out. “Stiff? Binary?” Becca stopped in the doorway. “Hey. Binary!”

Rick turned his head toward the door. “Becca?”

“Binary,” she repeated as she turned back. “Binary is zero (0) and one (1)…”


“Not necessarily two zeros, nor two ones.”

“Keep going…” Rick encouraged.

“In a binary system,” she paused, “there are four possible combinations of zero and one.” Becca put her laptop on rick’s desk then went to the whiteboard thinking, “Why do I have the feeling he’s going to be right again?” She wrote, 00, 01, 10, and 11 with a squeaky marker. “Two values, four combinations.”

“Keep going,” Rick said, “But use a different marker, please. How do you get four positions from…”

“From two cylinders?” Becca interrupted. “I got it! Two different sizes! Specifically two cylinders of different strokes.”

Rick stood up and smiled, “But what specific strokes?”

Becca wrote on the board, S(total) = S1 + S2.

“So,” Rick mentored slowly, “what combinations of S1 and S2 will give you…”

“Will give four equal spaces, three inches apart?” Becca drew and populated a table of values for all possible combinations. “Yes! Three and six?”

A relieved smile grew on Ricks face.

She turned and exclaimed, “One three inch, and one six inch cylinder!”

“You see,” Rick said. “I knew you would figure it…”

Becca interrupted, “You knew that all along, didn’t you?”

“No,” Rick rubbed his nose. “It was really you.”

Mentor Discussion and Exercises

Conversation, study, and new perspectives often reveal additional solutions.

  1. Draw and populate the binary table to show four equally spaced lengths given two cylinders of different strokes.
  2. Why didn’t Rick specify the use of cylinders in his specification?
  3. What other methods could be used to achieve cost effective equal spaced actuator positioning?
  4. If mounting two cylinders end to end makes the overall assembly too big, what other cylinder mounting configurations could be used?
  5. Why do 3D Printers often have multiple filament spools?


About Kenneth Richard Hardman

AncestorClips are very short stories about very real people. Each clip nurtures awareness of a time, a place, and the character of a man or woman who cultivated a path for our life. The reader feels the good, the obstacles, the happiness, the sadness, and the overcoming. They cheer us, make us resilient when challenged, give us purpose, and connect us to our multi-generational family. Each story is followed by reflections from the author and readers sharing how the story strengthened or inspired them. Ken Hardman is a son, a brother, a grandson, a great-grandson… He is also a husband, father and grand-father. Ken is a professional engineer, engineering mentor, technical writer, and associate technical fellow at a major aerospace company. He is a writer of engineering and family history stories. Please join Ken in reading, reflecting upon, or writing #AncestorClips
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1 Response to One + One-half = Four

  1. Pingback: Too binary in your engineering thinking? | Engineering Stories

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