KIGAKU

Ten visual simulations on gears, pulleys, levers, linkages, cams, slider-crank, screws, hydraulics, belts, and a 2-link robot arm. Touch the mechanisms.

KIGAKU is a visual education app on machine elements and mechanisms. Volume 15 of the "RAKU" series.

The "RAKU" series has covered math (SUUGAKU), physics, electricity, waves, heat, stars, light, quantum, fluid, probability, geometry, chemistry, microbes, and brain. Each title makes one discipline tangible by letting you see and move the ideas. KIGAKU does the same for the machines humans have built - from a pair of meshing gears to a 2-link robot arm.

While the sister app BUTURAKU covers natural physical phenomena, KIGAKU focuses on engineered mechanisms.

[Ten Simulations]

• Gear Two meshing spur gears that show how tooth counts change the trade-off between speed and force. Vary Z1, Z2, and the input RPM and watch the speed ratio and torque ratio respond inversely - the bigger gear turns slower, with proportionally more torque.

• Pulley A block-and-tackle that lets you lift a load with less force - in exchange for pulling a longer distance. Vary the supporting rope count N (1-6) and see how the required force W/N shrinks while the rope you must pull grows by the same factor, with total work conserved.

• Lever Drag the fulcrum and see how a beam trades force for distance. Switch between 1st-, 2nd-, and 3rd-class levers, with the moment balance F1L1 = F2L2 holding at every position.

• Linkage A four-bar linkage that turns rotation into complex motion. Change the bar lengths and watch how the path changes in real time. The mechanism type - crank-rocker, double-crank, or double-rocker - switches automatically based on Grashof's condition, with the coupler-point curve traced live.

• Cam A rotating cam that drives a follower smoothly up and down. Watch how the cam's outline shapes the motion above it - a cycloidal profile gives a particularly smooth ride, with the relation between cam shape and follower motion shown side by side.

• Crank The mechanism that turns rotation into back-and-forth piston motion - the heart of every internal combustion engine. Vary the crank radius r and connecting-rod length l and see how the ratio r/l deforms the piston motion away from a pure sine wave (its second-harmonic component).

• Screw A power screw / screw jack that converts a small torque into a large thrust - the same principle as car jacks and clamps. Tune the lead L, input torque T, and efficiency η (eta) and read the resulting force F = 2π·T·η/L; a smaller lead means more force, at the cost of speed.

• Hydraulic Pascal's principle - a small input force becomes a large output force when fluid pressure is shared across cylinders of different sizes. Vary the input and output piston diameters; the area ratio A2/A1 becomes the force multiplication, with the output stroke shrinking by the same factor - the foundation of construction machines and brakes.

• Belt Drive Two pulleys connected by a belt - the speed ratio is simply the diameter ratio D1/D2. The same principle behind bicycle gears and machine spindles.

• Robot Arm A 2-link planar robot arm where joint angles decide where the tip goes. Move the shoulder and elbow joints (θ1, θ2) and watch the tip position (x, y) update in real time - the basics of forward kinematics, with the reachable workspace drawn.

[Features]

• Each screen pairs the simulation with formulas and historical context
• Textbook-level implementations of gear ratios, lever moments, Pascal's principle, forward kinematics, and more
• Japanese / English UI
• Dark / Light mode
• Clean, intuitive Material Design 3 UI
• Banner ad at the bottom only - no interstitials, no rewarded ads

[Who it's for]

• Students of mechanical engineering, robotics, and mechatronics
• Self-taught engineers refreshing their intuition
• Science teachers building visual demonstrations