Recent Blogs
Water Wheel Form 4: Current-Wheel Animation and Power Calculator
Explore a current-driven wheel and calculate a uniform-flow power scenario using entered capture area, power coefficient, tip-speed ratio and diameter.
Water Wheel Form 3: Overshot Animation, Power and Energy Calculator
Calculate an overshot-wheel power scenario from steady flow, net head and entered efficiency. Compare torque at chosen rpm and energy for constant 24-hour operation.
Water Wheel Form 2: Pitchback Animation and Power Calculator
Calculate power from flow and net head for an illustrated pitchback wheel. Rpm and torque use an explicit fixed rim-speed assumption of 1.8 m/s.
Water Wheel Form 1: Overshot Animation and Static-Moment Calculator
Explore an overshot wheel and calculate the moment of an entered retained water mass, then compare power at a chosen speed. Flow and head are...
Tread Mill: Static Gravity Moment and Rim-force Equivalent
Explore a treadwheel with a static point-load model. Calculate gravity moment and equivalent rim force from mass and horizontal offset, without predicting power.
Breast-Shot Paddle Wheel: Declared Breast-Arc Layout
Explore a breast-shot wheel layout. Calculate circumference, paddle spacing, rim pitch and arc length at the wheel radius from diameter, count and arc angle.
Undershot Paddle Wheel: Declared Radial-Paddle Layout
Explore undershot paddle-wheel geometry. Calculate circumference, equal paddle spacing, rim arc pitch and one rectangular paddle-face area.
Barker's Mill / Water Wheel: How This Reaction Turbine Works, Parts, Formula and Uses Explained
How a Barker's Mill water wheel works — reaction-driven rotation, design formulas, real-world applications in milling and hydropower demonstrations.
Two-degree Cylindrical Pair: Independent Sliding and Rotation
Explore independent axial sliding and rotation in a cylindrical pair. Compare entered geometric ratios and a simple friction estimate; jamming is not predicted.
Spherical Pair Mechanism Explained: How a Ball-and-Socket Joint Works, Diagram, Parts, and Uses
Spherical pair explained — how a ball-and-socket joint delivers 3 rotational DOF with zero translation, with formulas, real robotics examples and tolerances.
Sliding-and-rotating Prism in Cylinder: How This Two-DOF Kinematic Pair Works, Parts, and Uses
Explore independent rotation and sliding of a hexagonal prism in a circular bore. Calculate its ideal corner envelope, section area and engagement ratio.
Roller-on-cam Higher Pair Mechanism: How It Works, Diagram, Pressure Angle and Uses Explained
Roller-on-cam higher pair explained — contact geometry, pressure angle, and sizing for automotive valvetrains, indexers, and packaging cams. With worked example.
Prismatic Pair: Declared Sliding-Friction Ledger
Prismatic Pair explained — the sliding lower-element joint behind every Linear Actuator, machine slide and hydraulic cylinder. Specs, formulas, real builds.
Planar Pair: Exact Three-Coordinate Pose Geometry
Planar Pair explained — the plane-on-plane kinematic pair gives 3 DOF in machine-tool slides, surface grinders, and flatbed printers. Formula, examples, tradeoffs.
Hyperboloid Pair: Ideal Effective-Radius Ratio Calculator | FIRGELLI
Compare ideal speed and torque ratios for two effective rolling radii. The tangent-circle illustration does not design hyperboloid surfaces, teeth or skew-axis contact.
Helical Gear Pair: Ideal Force-Component Calculator | FIRGELLI
Calculate tangential and axial force magnitudes from torque, pitch diameter and helix angle. Contact ratio is entered, and gear strength and bearing life are not...
Gear-Tooth Higher Pair: Involute Gear Geometry Calculator | FIRGELLI
Calculate nominal spur-gear ratio, driven speed, centre distance and pitch-line speed. Explore how pressure angle changes the base circles and line of action.
Cylindrical Pair (revolute) Mechanism Explained: How It Works, Diagram, and Uses
Explore a journal with axial retaining collars. Calculate projected bearing area, nominal radial pressure and length-to-diameter ratio from load and dimensions.
Cylinder-on-cylinder Lower Pair Mechanism: How It Works, Diagram, Parts and Uses Explained
Explore independent sliding and rotation in a cylindrical joint. Compare bore and shaft diameters to calculate signed radial and diametral clearance.
Cone-on-cone Rolling Pair Mechanism: How It Works, Parts, Formula and Uses Explained
Explore ideal rolling cones with a shared apex. Compare cone angles, shaft angle and speed ratio, with apex offset shown as a separate length comparison.
Cam-and-follower Higher Pair Mechanism: How It Works, Diagram, Parts, Formula and Uses Explained
Explore a harmonic disk cam and guided knife-edge follower. Compare lift, peak speed and pressure angle, with equations and a worked example matching the calculator.
Screw Pair Mechanism: How It Works, Diagram, Lead Formula, Parts, and Uses Explained
Screw Pair explained — how helical threads convert rotation into linear motion, with lead/pitch math, real applications in machining, and design tradeoffs.
Screw-cutting/slide Lathe Motion: How It Works, Diagram, Parts, Formula and Uses Explained
Screw-cutting lathe motion synchronises spindle rotation to carriage travel through a leadscrew and gear train, letting machinists cut precise threads on metal lathes.
Screw-cutting Variable Pitch Mechanism Explained: How It Works, Diagram, Formula and CNC Uses
Screw-cutting with variable pitch lets machinists generate threads whose lead changes along the axis. Learn the lathe gearing, math, and applications.
Screw Stamping-press Mechanism: How It Works, Diagram, Parts, Formula and Uses Explained
Explore a weighted-handle screw press and compare rotational kinetic energy at two selected speeds with unchanged inertia.