🦾 Two-Joint Angle Bench: step-by-step build

Separate a lower arm’s joint angle from its direction relative to the table.

A lower arm can turn twice: once at its own hinge and once because its upper arm carries it. This original serial two-hinge bench makes relative and absolute angles visible with retained stock beams. Its gentle chosen animation is kinematics, not chaotic pendulum dynamics or a prediction of natural timing.

  • Level 3 of 5 (medium)
  • About 30 minutes
  • 12 steps, 27 parts
  • Powered by: Hand-crank
  • Series: Starter Builds

What you will learn

  • Linkages: Beams joined by pins change one motion into another.
  • Pendulum: A hanging weight swings back toward its lowest point.
  • Axles: An axle is a cross-shaped rod — anything on it turns together.
  • Bushes & Spacers: Bushes stop things sliding off an axle.
  • Frames: A frame is a ready-made strong rectangle.
  • Pins: Grippy or Smooth: Pins join beams together — some hold tight, some let things swing.
  • Centre of Gravity: Keep the heavy stuff low and in the middle and your model won't tip.

Build these first

  • ↔️ Pivot Position Bench: Two equal beams hang from different holes: compare their gravity lever arms. (level 2 of 5, about 20 minutes, 11 steps)

Parts you need

  • 1 × Open frame 5×7
  • 4 × Blue long pin
  • 4 × Split pin block
  • 4 × Red axle-pin
  • 2 × Beam 11
  • 1 × Axle 12
  • 8 × Half bush
  • 1 × Beam 5
  • 1 × Axle 6
  • 1 × Beam 3

Steps

  1. Lay the 5×7 frame flat on a level table. Its two short ends will carry separate rigid posts.
  2. Insert two blue long pins upward through the second and fourth holes of the back short end. Fit two split pin blocks one above the other onto the same pins.
  3. Put a red axle pin in each back block’s centre cross hole, pointing backward. Two fixing points stop the post tipping.
  4. Stand an 11-hole beam at the back. Fit its second and third holes onto the back pair of red axle pins.
  5. Pass a 12-module axle through the back post’s ninth hole, eight hole spacings above its bottom hole. Fit one half bush immediately outside the back post. Slide another to the middle, against the back face of the future yellow beam.
  6. Slide the top round hole of a yellow five-hole beam onto the main axle in the rear swinging lane, hanging downward. Seat a half bush against its front face. The rear spacer already fitted and this front spacer retain the beam without keying it.
  7. Pass a six-module axle through the bottom round hole of the yellow arm. Position it with two hole spacings extending behind the yellow arm’s centre plane and four in front. Seat half bushes against both faces of the yellow beam; this retains the complete joint shaft. Support the arm temporarily while fitting the pieces.
  8. Slide another half bush onto the front of the joint shaft until it meets the front yellow-arm spacer. These two half bushes sit back to back. Hang a red three-hole beam from its top round hole against this new spacer, with its lower end down. Add a final half bush against the red beam’s front face. Both beams rotate around the shaft; caps grip only the axle. Check free motion without axial escape.
  9. Now add the front block pair: two blue long pins upward through the second and fourth holes, then two split pin blocks stacked on them. Adding these after the pendulum keeps its insertion path open.
  10. Fit two red axle pins pointing forward in the front blocks’ centre cross holes.
  11. Fit the front 11-hole post onto its two red axle pins while guiding the long axle through its ninth hole. The two posts are eight modules apart, supporting both ends of the pivot axle.
  12. Add a final half bush just outside the front post. The outside half bushes retain the axle in both directions; the four middle spacers retain the two swinging beams. Check every block and pin is firmly seated.

Play time

Hold only the stationary frame. Gently set the upper arm within fifteen degrees of down and the lower hinge within fifteen degrees relative to that arm. Compare the lower arm with a vertical reference beside the model, clear of moving parts. No physical stops are fitted. Stop for rubbing or any loose retainer. Do not force, motorize or invert this model. No physical prototype or natural timing measured.

Credited demonstrations and component sources

  • LEGO DOUBLE PENDULUM — Shafie Shahrin: Independent serial-arm demonstration inspires our relative-versus-absolute angle question. Our original retained stock-parts bench is not its design or a chaotic-motion replica.
  • myPhysicsLab — Double Pendulum kinematics: Primary derivation of planar pin-centre position with absolute angles. Our lower absolute angle is upper plus relative; only geometry is modeled, not its point-mass dynamics.