Motion analysis: plots of a study's joint values and a point's path, and the parts that collide along it
- motion.plot: joint values and a point's path sampled as the study plays (closed loops following), with velocities and accelerations by finite differences, per step or per second with a duration. - motion.interference: the pairs of parts that pass through each other along a study, with the first step, the step ranges, the depth and the shared volume; occurrences, against or contact sets choose the pairs; bounded samples and work. - Motion Study dialog: a Study box opens a saved study; a chart of a joint value or a picked point with a cursor at the step shown (click to move there); Check collisions with the steps shaded on the chart. ui.start motion.study takes study.
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//! `motion.plot` against the analytic motion of a four-bar and a slider-crank, and
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//! `motion.interference` on two blocks pushed through each other at a known step.
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use serde_json::{Value, json};
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use solidcraft_geom::Vec3;
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use super::{four_bar, occ, rocker_pin, run, slider_crank};
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use crate::Session;
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/// A joint's series in a plot, by joint name.
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fn series<'a>(r: &'a Value, name: &str) -> &'a Value {
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r["joints"].as_array().and_then(|list| list.iter().find(|j| j["name"] == name)).unwrap_or(&Value::Null)
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}
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fn nums(v: &Value) -> Vec<f64> {
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v.as_array().into_iter().flatten().map(|x| x.as_f64().unwrap_or(f64::NAN)).collect()
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}
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/// The crank turns at a constant 50°/s (a full turn in 7.2 s). The rocker turns at
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/// ω4 = ω2·a·sin(θ2 − θ3) / (c·sin(θ4 − θ3)) (crank a = 20, rocker c = 40; θ2, θ3 and θ4 the
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/// crank, coupler and rocker angles), from differentiating the loop a·e^iθ2 + b·e^iθ3 = d + c·e^iθ4.
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#[test]
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fn four_bar_rocker_velocity_matches_its_analytic_derivative() {
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let (mut s, _, q0) = four_bar();
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run(&mut s, "motion.study", json!({"name": "Turn", "steps": 360, "keys": [{"joint": "Crank", "points": [[0, 0], [360, 360]]}]}));
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let before = s.doc.clone();
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let r = run(&mut s, "motion.plot", json!({"study": "Turn", "joints": ["Crank", "Rocker"], "samples": 181, "duration": 7.2}));
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assert_eq!(*s.doc, *before, "a plot leaves the design as it was");
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assert!(r["stopped_at"].is_null() && r["samples"] == 181, "{}", r["stopped_by_loop"]);
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assert_eq!(r["joints"].as_array().map(Vec::len), Some(2));
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let (crank, rocker) = (series(&r, "Crank"), series(&r, "Rocker"));
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assert_eq!((rocker["unit"].as_str(), rocker["velocity_unit"].as_str()), (Some("deg"), Some("deg/s")));
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let time = nums(&r["time"]);
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assert!((time.last().copied().unwrap_or(0.0) - 7.2).abs() < 1e-9 && (time[1] - 0.04).abs() < 1e-12, "{time:?}");
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// The crank: exactly as keyed, at a constant speed.
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for ((v, w), a) in nums(&crank["value"]).iter().zip(nums(&crank["velocity"])).zip(nums(&crank["acceleration"])) {
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assert!((w - 50.0).abs() < 1e-6 && a.abs() < 1e-6, "{v}°: {w} deg/s, {a} deg/s²");
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}
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let (value, velocity) = (nums(&rocker["value"]), nums(&rocker["velocity"]));
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let start = q0.y.atan2(q0.x - 45.0);
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let (mut q, mut peak, mut worst) = (q0, 0.0f64, 0.0f64);
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for k in 0..181 {
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let v = 2.0 * k as f64;
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if k > 0 {
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q = rocker_pin(v - 2.0, v, q);
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}
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let th2 = (90.0 + v).to_radians();
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let p = Vec3::new(20.0 * th2.cos(), 20.0 * th2.sin(), 0.0);
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let (th3, th4) = ((q - p).y.atan2((q - p).x), q.y.atan2(q.x - 45.0));
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// The rocker's value is its turn from where it was assembled, made continuous.
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let turned = (th4 - start).to_degrees();
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assert!(((value[k] - turned + 540.0).rem_euclid(360.0) - 180.0).abs() < 1e-6, "{v}°: {} wants {turned}", value[k]);
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let w4 = 50.0 * 20.0 * (th2 - th3).sin() / (40.0 * (th4 - th3).sin());
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peak = peak.max(w4.abs());
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worst = worst.max((velocity[k] - w4).abs());
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}
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// Central differences 0.04 s apart: within 0.2 % of the fastest swing.
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assert!(peak > 40.0 && worst < 2e-3 * peak, "worst {worst} deg/s of {peak} deg/s");
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}
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/// The piston of a slider-crank (crank a = 15, rod b = 40) turning at 100°/s sits at
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/// x = a·cos θ + S with S = √(b² − a²·sin²θ), so it accelerates at
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/// ω²·(−a·cos θ − a²·cos 2θ / S − a⁴·sin²θ·cos²θ / S³).
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#[test]
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fn slider_crank_piston_acceleration_matches_its_analytic_form() {
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let (mut s, _, s0) = slider_crank();
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run(&mut s, "motion.study", json!({"name": "Turn", "steps": 360, "keys": [{"joint": "Crank", "points": [[0, 0], [360, 360]]}]}));
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let p = json!({"study": "Turn", "joints": ["Bore"], "occurrence": "Piston", "point": [s0.x, s0.y, s0.z], "samples": 181, "duration": 3.6});
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let r = run(&mut s, "motion.plot", p);
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assert!(r["stopped_at"].is_null() && r["samples"] == 181, "{}", r["stopped_by_loop"]);
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let point = &r["point"];
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assert_eq!((point["occurrence"].as_str(), point["acceleration_unit"].as_str()), (Some("Piston:1"), Some("mm/s²")));
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let at = |key: &str, k: usize, c: usize| point[key][k][c].as_f64().unwrap_or(f64::NAN);
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let (a, b, w) = (15.0f64, 40.0f64, 100.0f64.to_radians());
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let (mut peak, mut worst) = (0.0f64, 0.0f64);
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for k in 0..181 {
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let th = (90.0 + 2.0 * k as f64).to_radians();
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let root = (b * b - (a * th.sin()).powi(2)).sqrt();
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assert!((at("position", k, 0) - (a * th.cos() + root)).abs() < 1e-6, "{k}");
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let want = w * w * (-a * th.cos() - a * a * (2.0 * th).cos() / root - a.powi(4) * (th.sin() * th.cos()).powi(2) / root.powi(3));
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peak = peak.max(want.abs());
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// The ends take one-sided differences; inside, central ones.
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let tolerance = if k == 0 || k == 180 { 2e-2 } else { 2e-3 };
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worst = worst.max((at("acceleration", k, 0) - want).abs() / tolerance);
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assert!(at("acceleration", k, 1).abs() < 1e-6 && at("acceleration", k, 2).abs() < 1e-6, "it stays on its axis");
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}
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assert!(peak > 40.0 && worst < peak, "worst {worst} of {peak} mm/s² (scaled by tolerance)");
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// The bore's value is the piston's travel, so its acceleration is the piston's along x.
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let bore = series(&r, "Bore");
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assert_eq!(bore["acceleration_unit"], "mm/s²");
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let along = |k: usize| nums(&bore["value"])[k] - nums(&bore["value"])[0];
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let sign = if along(90) * (at("position", 90, 0) - at("position", 0, 0)) < 0.0 { -1.0 } else { 1.0 };
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for (k, acc) in nums(&bore["acceleration"]).iter().enumerate() {
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assert!((acc - sign * at("acceleration", k, 0)).abs() < 1e-6, "{k}: {acc}");
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}
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// Per step without a duration: 2 steps between samples, 1° a step.
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let r = run(&mut s, "motion.plot", json!({"study": "Turn", "joints": ["Crank"], "samples": 181}));
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let crank = series(&r, "Crank");
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assert!(r["time"].is_null() && crank["velocity_unit"] == "deg/step", "{crank}");
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assert!(nums(&crank["velocity"]).iter().all(|v| (v - 1.0).abs() < 1e-9));
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}
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/// Cubes A (grounded, x 0…10) and B (x 20…30) on a slider along x, B 10 mm away at value 10.
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fn rail() -> Session {
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let mut s = Session::default();
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for (name, x) in [("A", 0), ("B", 20)] {
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run(&mut s, "component.activate", json!({"component": "root"}));
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run(&mut s, "component.create", json!({"name": name}));
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run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [x, 0, 0]}));
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}
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run(&mut s, "component.activate", json!({"component": "root"}));
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let a = occ(&s, "A");
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run(&mut s, "occurrence.ground", json!({"occurrence": a, "grounded": true}));
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run(&mut s, "joint.create", json!({"type": "slider", "a": {"face": [10, 5, 5]}, "b": {"face": [20, 5, 5]}, "name": "Rail"}));
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run(&mut s, "joint.drive", json!({"joint": "Rail", "value": 10}));
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s
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}
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/// B is pushed 1 mm a step from 10 mm away to 5 mm into A: the faces touch at step 10 and the
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/// blocks overlap from step 11 to the end, 100 mm³ more each step.
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#[test]
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fn interference_names_the_step_two_parts_start_to_collide() {
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let mut s = rail();
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run(&mut s, "motion.study", json!({"name": "Push", "steps": 15, "keys": [{"joint": "Rail", "points": [[0, 10], [15, -5]]}]}));
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// A contact set would stop the motion where the faces touch; the check plays through.
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run(&mut s, "contact.create", json!({"occurrences": ["A", "B"]}));
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let before = s.doc.clone();
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for p in [json!({"study": "Push"}), json!({"study": "Push", "occurrences": ["A", "B"]}), json!({"study": "Push", "contact_sets": true})] {
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let r = run(&mut s, "motion.interference", p.clone());
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assert_eq!(*s.doc, *before, "the design is left as it was");
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assert!(r["clear"] == false && r["samples"] == 16 && r["pairs"] == 1 && r["truncated"] == false, "{p}: {r}");
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let c = &r["collisions"][0];
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assert_eq!((c["a"].as_str(), c["b"].as_str()), (Some("A:1"), Some("B:1")), "{r}");
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assert_eq!((c["first_step"].as_f64(), c["last_step"].as_f64()), (Some(11.0), Some(15.0)), "{r}");
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assert_eq!(c["steps"], json!([[11.0, 15.0]]), "{r}");
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let deepest = c["deepest_step"].as_f64().unwrap_or(f64::NAN);
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assert!(c["depth_mm"].as_f64().unwrap_or(0.0) > 1.0 && (11.0..=15.0).contains(&deepest), "{r}");
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let volume = c["volume_mm3"].as_f64().unwrap_or(f64::NAN);
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assert!((volume - 100.0 * (deepest - 10.0)).abs() < 1e-6, "{r}");
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}
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// B against a far block C only: B's pass through A is not asked about.
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run(&mut s, "component.create", json!({"name": "C"}));
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run(&mut s, "solid.box", json!({"length": 10, "width": 10, "height": 10, "corner": [0, 50, 0]}));
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run(&mut s, "component.activate", json!({"component": "root"}));
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let r = run(&mut s, "motion.interference", json!({"study": "Push", "occurrences": ["B"], "against": ["C"]}));
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assert!(r["clear"] == true && r["pairs"] == 1, "{r}");
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let r = run(&mut s, "motion.interference", json!({"study": "Push", "occurrences": ["B"], "against": ["A", "C"]}));
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assert!(r["pairs"] == 2 && r["collisions"].as_array().map(Vec::len) == Some(1) && r["collisions"][0]["first_step"] == 11.0, "{r}");
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assert!(s.execute("motion.interference", &json!({"study": "Push", "against": ["A"]})).is_err());
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// Pushed only to touching, they never pass through each other.
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run(&mut s, "motion.study", json!({"study": "Push", "keys": [{"joint": "Rail", "points": [[0, 10], [15, 0]]}]}));
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let r = run(&mut s, "motion.interference", json!({"study": "Push"}));
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assert!(r["clear"] == true && r["collisions"] == json!([]), "{r}");
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}
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/// Hostile parameters are refused, never a panic.
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#[test]
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fn motion_analysis_refuses_what_it_cannot_do() {
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let mut s = rail();
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run(&mut s, "motion.study", json!({"name": "Push", "steps": 15, "keys": [{"joint": "Rail", "points": [[0, 10], [15, -5]]}]}));
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let refused = [
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("motion.plot", json!({"study": "Nope"})),
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("motion.plot", json!({"study": "Push", "samples": 2})),
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("motion.plot", json!({"study": "Push", "samples": 1e9})),
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("motion.plot", json!({"study": "Push", "samples": "many"})),
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("motion.plot", json!({"study": "Push", "duration": 0})),
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("motion.plot", json!({"study": "Push", "duration": -3})),
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("motion.plot", json!({"study": "Push", "joints": ["Nope"]})),
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("motion.plot", json!({"study": "Push", "joints": vec![json!("Rail"); 300]})),
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("motion.plot", json!({"study": "Push", "point": [1, 2]})),
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("motion.plot", json!({"study": "Push", "occurrence": "B", "point": [1e300, 0, 0]})),
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("motion.interference", json!({"study": "Push", "samples": 1})),
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("motion.interference", json!({"study": "Push", "samples": f64::MAX})),
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("motion.interference", json!({"study": "Push", "occurrences": ["A"]})),
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("motion.interference", json!({"study": "Push", "occurrences": ["A", "B"], "contact_sets": true})),
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("motion.interference", json!({"study": "Push", "contact_sets": true})),
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];
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for (cmd, p) in refused {
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assert!(s.execute(cmd, &p).is_err(), "{cmd} {p}");
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}
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// A point of a part that does not move has no velocity.
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let r = run(&mut s, "motion.plot", json!({"study": "Push", "occurrence": "A", "point": [5, 5, 5]}));
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assert!(r["point"]["speed"].as_array().is_some_and(|v| v.len() == 16 && v.iter().all(|x| x.as_f64() == Some(0.0))), "{r}");
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}
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