How Planar Squinetics works
Build a mechanics problem out of parts, then press ▶ to watch it move. Every force is worked out exactly from Newton's second law, ΣF = ma, the same way you'd solve it on paper, so the numbers are the textbook answers.
Building
- The build tools are down the left side. Block: click to drop one. Near a floor, ramp, table or another block it sits on it; higher up it hangs in the air (for ropes, pendulums and projectiles).
- Ramp, Table, Wall: click where they go. Blocks slide off tables and up or down ramps, and bump into walls.
- Pulley and Hook: click to place. A pulley can have mass (then the rope's tension is different on each side). Every wheel turns as the rope runs over it.
- Rope: click where it starts, then each pulley it goes over, then where it ends. An end can be a block, a hook, any empty spot (a hook appears there), or a point on another rope (it gets a knot that moves with the rope). Start a rope on a wheel, or click its last wheel twice, to wind it round that wheel like a spool. Ropes stay taut and go slack on their own.
- Spring: click its two ends: blocks, hooks, walls, any empty spot, a point on a rope, or a wheel. Click near a wheel's edge to tie it to the rim (it turns with the wheel), or near the middle for the axle. Set its stiffness k and natural length.
- Force: press on a block and drag the way you want to push or pull it. The arrow follows you and shows the size (10 N for every metre you drag) and angle; it clicks onto every 15°. Just click for a 10 N push. You can fine-tune the numbers afterwards.
- Shapes (the ▬ button: rod, disk, plate, triangle, or draw your own outline corner by corner) are rigid bodies that turn as well as move. Select one to get a square handle (resize) and a circle (turn). Shapes can be fixed in place, too, to make ground of any shape.
- Joint: click a shape or block for a joint on it that moves with it (ropes and springs tie there; a block pinned off its middle can turn), where two shapes overlap to pin them together, or empty space for a free joint to tie ropes, springs and shapes to (so a rope and a spring can meet). Right-click a joint to fix it in place. Click a joint to make it a pin (turns freely), a weld (locked) or a motor (turns at a set speed). Shapes joined together pass through each other; separate shapes bump. Ropes and springs tie to any point on a shape.
- Damper (under Spring): click its two ends like a spring. It pushes back against how fast it's stretched or squeezed (F = c·v), slowing things down and turning their motion into heat. Give a spring some damping c, or a damper some stiffness k, and you get a spring and damper side by side.
- Shaking support: right-click a hook and pick Shakes back and forth. It moves by u(t) = A·sin(2πf·t) along the direction you set, shaking whatever is tied to it (a spring, a damper, a joint), for driven vibrations and resonance.
- Slider: right-click a joint and pick Slider. The shape or block slides along the rail it's joined to (the longer shape, or a straight track on the background) and turns with it, with no friction, and stops at the rail's ends. Tie a spring along it for a mass on a sprung slide.
- Bumper (under Spring): a spring held down at one end only. Click its base, then where its free end reaches. Anything that runs into it squashes it.
- Select: click anything to change its numbers on the right; drag to move it, or drag its square handle to resize a block, table, wall, ramp or shape. Drag empty space to move around; scroll (or pinch) to zoom. After you place anything, you're back in Select.
- Pick many: drag a box around shapes and blocks to pick everything wholly inside it (Shift adds more), or click them one at a time (click again to take one out), then group them into one shape, or cut one out of another as a hole.
- Variables: any number box takes an expression like 2M or M + 0.5. A new letter becomes a variable you can change at the top of the panel, and everything that uses it follows. The Solve tab can solve for a variable.
- Numbers that move: in any number box that can change as it runs (a spring's k, a force, a motor's speed, a block's friction) you can type an expression in t (time, in seconds) like 3t or 2 sin(180t), and in sensors that read another thing's state: speed(A), xpos(A), ypos(A), xvel(A), yvel(A), omega(wheel), angle(Rod1), force(spring1) (name a block by its letter, anything by its id). They're worked out again at every step, so one number can drive another: a force that grows with speed, a motor that slows as a block nears.
- Pair rules (right-click → Pair rules…): a magnet pulls two things together or pushes them apart (k newtons at 1 m), and a one-way gate lets things through only while they move a set way (a platform you can jump up through). Passes through… turns collisions off between particular pairs, or for everything.
- Sweep (Solve tab): plot how any result changes as you vary one number, optionally after running for a few seconds.
- Snap to grid (View menu) lines everything up as you place and drag it; pick how far apart the snap points are there too.
- Shapes: right-click a drawn shape and pick Tidy shape to straighten it (a nearly regular shape becomes regular, near-right angles square, near-equal sides equal). Shapes picked together can be grouped into one, or one cut out of another as a hole that other shapes can sit inside. The Corners slider rounds a shape off. Click an existing joint with the Joint tool to join another shape at that same point.
- Crossing trace: right-click a point on one shape and pick Use this point's x, then a point on another and pick Use this point's y. Press ▶ and it draws where a line straight up from the first meets a line straight across from the second: circles on circles and spinning rods make drawings this way.
- Right-click anything (or press and hold on a phone) for its options: make a pulley free to move (a movable pulley) or locked so it doesn't turn, hang a rope from a pulley's axle, make a hook a free joint, Track movement to draw the path something takes, duplicate or delete. Right-click empty space to add a block, pulley or hook there.
Reading it
- The View menu turns on each block's free-body diagram (on to start with): weight mg, normal force N, friction f (static fₛ or kinetic fₖ), tension T, spring force and applied forces.
- Inspect lists every force on the selected block and writes out ΣF = ma along the surface and across it, with the numbers plugged in. With nothing selected it shows energy and momentum. Heat is energy turned into warmth: by friction, by bumps that don't fully bounce, and by a rope or pulley stopping something with a jolt. Add it in and the total stays the same.
- The graphs show the selected block's position, velocity and acceleration over time. Hover them to read values.
Solving for unknowns
On Solve, tick the quantities you don't know (a mass, an angle, a coefficient of friction) and type in the ones you do know about the result (an acceleration, a tension, a normal force), one known for each unknown. Press Solve and it finds the unknowns. Results are for the instant the problem starts.
Assumptions
Blocks are treated as points (they slide; they don't tip). Ropes are light and don't stretch. Pulleys are frictionless; a pulley with mass is a uniform disk (I = ½MR²). Where a ramp meets the floor it's smooth, so speed carries through. Collisions use the restitution e: 1 bounces perfectly (elastic), 0 sticks together.
SquesmosPlanar Squinetics