Robot arms pass goods from belt to belt; native beam primitive

- Robot arm (category Industry): picks goods off the end of the nearest conveyor within its reach
  and puts them on the start of another conveyor within reach, or on a pallet a quarter turn on
  (pick / put: auto or a side). One move per item coming in (cycle 0) or a set cycle; waits while
  the line before it stands. The belt it feeds carries its goods at its pace and starts its loop
  when they land (feeds carry a time offset `ph`), so arm and belts stay in step.
- Drawn as a 16-pose flipbook: two-link inverse kinematics per pose, each pose shown for a
  sixteenth of the cycle by a stepped CSS animation (iso-flip; pose 0 alone when unanimated).
  Poses pointing away from the viewer are drawn before the base, the others after it.
- New sprite method beam(a, b, n, w, mat): a square bar between two 3D points, six faces culled
  and shaded like face(). Native, so the factory demo renders in 4.7 ms instead of 18.8 ms.
- Factory demo: a palletiser at the end of the carton line, a loading robot passing drums from the
  incline onto the loading belt into the truck. MCP instructions on robot arms.

Checks: 70 Rust tests (arms and belts in step, waiting arm, beam faces from every side),
Studio 109/109, web 90/90.

README.md

@@ -40,7 +40,7 @@ isokit build C:/dev/myproject/site-view   # dist/index.html, no server needed
 
 Try the demos: `isokit studio examples/demo` (a works site),
 `isokit studio examples/house` (a furnished house built from parts) and
-`isokit studio examples/factory` (presses and conveyors).
+`isokit studio examples/factory` (presses, conveyors and robot arms).
 
 ### Studio (for everyone)
 
@@ -196,8 +196,10 @@ storey.
 Production lines: a Producer (category Industry) makes goods at a set rate
 and puts them out on its +x side; Conveyors drawn from there carry them on,
 round corners and up inclines, each at its own speed, so the gap between goods
-follows rate and speed. Tooltips show the numbers. `examples/factory` (Factory
-demo in the web Studio) has a few lines.
+follows rate and speed. A Robot arm placed past a belt's end picks the goods
+off and puts them on the next belt or a pallet, in step with them. Tooltips
+show the numbers. `examples/factory` (Factory demo in the web Studio) has a
+few lines.
 
 Animations (fans, smoke, fish, traffic) step on about ten times a second by
 default ("light"): running CSS animations repaint the whole drawing every frame,
@@ -231,7 +233,7 @@ studio/                the Studio GUI (served by `isokit studio`, and by the web
 web/                   web Studio shell: WASM backend for studio.js, projects, folders, zip, code editor
 examples/demo          demo project (works site)
 examples/house         house built from parts (walls, windows, doors, floors, furniture, roof)
-examples/factory       production yard: producers and conveyors
+examples/factory       production yard: producers, conveyors, robot arms
 deploy/Caddyfile       the web Studio's vhost on the buildfor.life web server (s1)
 ```
 

crates/isokit-core/src/render.rs

@@ -870,6 +870,35 @@ mod tests {
         }
     }
 
+    #[test]
+    fn beams_show_three_faces_from_any_side() {
+        for (a, b, n) in [
+            ([0.0, 0.0, 1.0], [4.0, 0.0, 1.0], [0.0, 1.0, 0.0]),
+            ([0.0, 0.0, 1.0], [0.0, -4.0, 1.0], [1.0, 0.0, 0.0]),
+            ([0.0, 0.0, 0.0], [0.0, 0.0, 3.0], [1.0, 0.0, 0.0]),
+            ([0.0, 0.0, 0.0], [2.0, 1.0, 3.0], [-1.0, 2.0, 0.0]),
+        ] {
+            for rot in 0..4u8 {
+                let mut sc = Scene::new();
+                let mut s = Sprite::new("arm", "");
+                s.beam(a, b, n, 0.4, "iso-robot");
+                sc.add_sprite("main", s);
+                let html = render(&sc, rot, &RenderOpts::default()).html;
+                // three faces; two when one side is seen edge-on (an oblique bar)
+                let faces = html.matches("iso-robot ").count();
+                let oblique = a[0] != b[0] && a[2] != b[2];
+                assert!(
+                    faces == 3 || (oblique && faces == 2),
+                    "{a:?}->{b:?} rot {rot}: {faces} faces"
+                );
+                assert!(
+                    html.contains("iso-robot iso-t"),
+                    "{a:?}->{b:?} rot {rot}: no top"
+                );
+            }
+        }
+    }
+
     #[test]
     fn faces_cull_and_shade_by_normal() {
         let mut sc = Scene::new();

crates/isokit-core/src/sprite.rs

@@ -388,6 +388,63 @@ impl Sprite {
         })
     }
 
+    /// A square bar `w` wide from `a` to `b` (robot arms, trusses): six faces,
+    /// culled and shaded by their normals like [`Sprite::face`]. `n` is a
+    /// side direction across the bar (any direction not along it).
+    pub fn beam(&mut self, a: P3, b: P3, n: P3, w: f64, mat: &str) -> &mut Self {
+        let sub = |p: P3, q: P3| [p[0] - q[0], p[1] - q[1], p[2] - q[2]];
+        let cross = |p: P3, q: P3| {
+            [
+                p[1] * q[2] - p[2] * q[1],
+                p[2] * q[0] - p[0] * q[2],
+                p[0] * q[1] - p[1] * q[0],
+            ]
+        };
+        let unit = |p: P3| {
+            let l = (p[0] * p[0] + p[1] * p[1] + p[2] * p[2]).sqrt();
+            if l < 1e-12 {
+                None
+            } else {
+                Some([p[0] / l, p[1] / l, p[2] / l])
+            }
+        };
+        let (Some(u), Some(v0)) = (unit(sub(b, a)), unit(cross(sub(b, a), n))) else {
+            return self;
+        };
+        // (u, n, v): a right-handed square frame, so every face below winds
+        // counter-clockwise seen from outside
+        let n = cross(v0, u);
+        let h = w / 2.0;
+        let c = |e: P3, sn: f64, sv: f64| {
+            [
+                e[0] + (n[0] * sn + v0[0] * sv) * h,
+                e[1] + (n[1] * sn + v0[1] * sv) * h,
+                e[2] + (n[2] * sn + v0[2] * sv) * h,
+            ]
+        };
+        let k = [
+            c(a, 1.0, 1.0),
+            c(a, -1.0, 1.0),
+            c(a, -1.0, -1.0),
+            c(a, 1.0, -1.0),
+            c(b, 1.0, 1.0),
+            c(b, -1.0, 1.0),
+            c(b, -1.0, -1.0),
+            c(b, 1.0, -1.0),
+        ];
+        for f in [
+            [1, 5, 4, 0],
+            [3, 7, 6, 2],
+            [3, 0, 4, 7],
+            [1, 2, 6, 5],
+            [3, 2, 1, 0],
+            [4, 5, 6, 7],
+        ] {
+            self.face(f.iter().map(|&i| k[i]).collect(), mat, None, false);
+        }
+        self
+    }
+
     /// 3D polygons as one path with a fixed class.
     pub fn poly(&mut self, polys: Vec<Vec<P3>>, cls: &str, id: Option<String>) -> &mut Self {
         let polys: Vec<Vec<P3>> = polys

crates/isokit-project/src/mcp.rs

@@ -27,7 +27,9 @@ meet, so for a plot boundary put each piece's ends exactly on the next piece's e
 Production lines (category Industry): a producer (props.rate per minute, product) puts goods out on its local +x \
 side; a conveyor (rot 0 runs towards +x, 90 +y, 180 -x, 270 -y; w = length, props.speed m/s) starting exactly \
 at that side carries them, and a conveyor whose start is at another's end carries on with them (corners join). \
-The gap between goods is speed / rate, so set the rate on the producer and the speeds on the belts.";
+The gap between goods is speed / rate, so set the rate on the producer and the speeds on the belts. \
+A robot_arm (props.reach, default 2 m) picks goods off the end of the nearest conveyor within its reach and puts \
+them on the start of another conveyor within reach, or on a pallet beside it; place it 1.5 to 2 m past a belt's end.";
 
 fn tool(name: &str, description: &str, props: Value, required: &[&str]) -> Value {
     json!({ "name": name, "description": description,

crates/isokit-script/src/api.rs

@@ -297,6 +297,14 @@ pub fn register_sprite(e: &mut Engine) {
             ok(s)
         },
     );
+    e.register_fn(
+        "beam",
+        |s: &mut SpriteH, a: D, b: D, nn: D, w: D, mat: &str| -> RR<SpriteH> {
+            s.0.borrow_mut()
+                .beam(p3(&a)?, p3(&b)?, p3(&nn)?, n(&w)?, &classes(mat));
+            ok(s)
+        },
+    );
     e.register_fn("face", |s: &mut SpriteH, p: D, mat: &str| -> RR<SpriteH> {
         s.0.borrow_mut().face(pts3(&p)?, &classes(mat), None, false);
         ok(s)

crates/isokit-script/src/tests.rs

@@ -643,6 +643,95 @@ fn conveyors_carry_what_the_producer_makes() {
     assert_eq!(row("belt3", "Speed"), "0.8 m/s");
 }
 
+fn robot_doc(belt1_running: bool) -> Doc {
+    let mut doc = Doc::default();
+    for (id, kind, x, y, rot, props) in [
+        ("press1", "producer", -6.0, -4.0, 0.0, json!({"rate": 15})),
+        (
+            "belt1",
+            "conveyor",
+            -1.4,
+            -4.0,
+            0.0,
+            json!({"w": 6, "running": belt1_running}),
+        ),
+        ("robot1", "robot_arm", 3.2, -4.0, 0.0, json!({})),
+        ("belt2", "conveyor", 3.2, 1.0, 90.0, json!({"w": 6})),
+        (
+            "robot2",
+            "robot_arm",
+            3.2,
+            5.8,
+            0.0,
+            json!({"colour": "mach2"}),
+        ),
+        (
+            "robot3",
+            "robot_arm",
+            -6.0,
+            5.0,
+            0.0,
+            json!({"running": false, "pick": "+x", "put": "-y", "goods": "drum"}),
+        ),
+    ] {
+        let mut o = obj(id, kind, x, y, props);
+        o.rot = rot;
+        doc.objects.push(o);
+    }
+    doc
+}
+
+#[test]
+fn robot_arms_pass_goods_from_belt_to_belt() {
+    let r = Runtime::new(&Bundle::default()).unwrap();
+    let doc = robot_doc(true);
+    for view in 0..4u8 {
+        let b = r.build("site", view, &cfg(), &doc).unwrap();
+        assert!(b.scene.warnings.is_empty(), "{:?}", b.scene.warnings);
+        let out = render(&b.scene, view, &RenderOpts::default());
+        assert_eq!(out.cycles, 0, "view {view}: depth-sort cycles");
+        assert!(!out.html.contains("NaN"));
+        // two running arms with 16 poses each, one shown at a time; the stopped one stands still
+        assert_eq!(
+            out.html.matches("iso-a iso-flip").count(),
+            32,
+            "view {view}"
+        );
+        assert_eq!(
+            out.html.matches("iso-flip iso-pose0").count(),
+            2,
+            "view {view}"
+        );
+    }
+    let b = r.build("site", 1, &cfg(), &doc).unwrap();
+    let out = render(&b.scene, 1, &RenderOpts::default());
+    let row = |id: &str, k: &str| {
+        out.info[id]
+            .rows
+            .iter()
+            .find(|r| r.0 == k)
+            .map(|r| r.1.clone())
+            .unwrap_or_default()
+    };
+    assert_eq!(row("robot1", "Moves"), "cartons from belt1 to belt2");
+    assert_eq!(row("robot1", "Cycle"), "4 s");
+    // the belt after the arm carries its goods at its pace, starting its loop when they land
+    assert_eq!(
+        row("belt2", "Carries"),
+        "15 cartons a minute, 2 m apart (from robot1)"
+    );
+    assert!(out
+        .html
+        .contains("animation-duration:4.0s;animation-delay:-1.75s"));
+    assert_eq!(row("robot2", "Moves"), "cartons from belt2 to a pallet");
+    assert_eq!(row("robot3", "Cycle"), "4 s (stopped)");
+    // a stopped belt before it: the arm waits
+    let b = r.build("site", 1, &cfg(), &robot_doc(false)).unwrap();
+    let out = render(&b.scene, 1, &RenderOpts::default());
+    assert_eq!(out.html.matches("iso-a iso-flip").count(), 0);
+    assert!(out.info["robot1"].rows[1].1.contains("waiting"));
+}
+
 #[test]
 fn site_walls_join_at_corners() {
     let r = Runtime::new(&Bundle::default()).unwrap();

crates/isokit-script/stdlib/industry.rhai

@@ -1,7 +1,9 @@
-// isokit/industry: conveyors and producers (machines that make goods at a
-// set rate). Goods flow from a producer onto the conveyor starting at its
-// output and on along the conveyors that start where another one ends: each
-// belt carries them at its own speed, so the gap between them is speed / rate.
+// isokit/industry: conveyors, producers (machines that make goods at a set
+// rate) and robot arms. Goods flow from a producer onto the conveyor starting
+// at its output and on along the conveyors that start where another one ends:
+// each belt carries them at its own speed, so the gap between them is
+// speed / rate. A robot arm picks them off the end of a belt in its reach and
+// puts them on the start of another belt, or on a pallet.
 
 fn goods_kinds() { ["carton", "crate", "drum", "sack", "part"] }
 
@@ -67,10 +69,12 @@ fn conveyor_ext(o, e) {
     0.0
 }
 
-/// What reaches conveyor o at its start: #{ rate, item, running, from }
-/// (rate in goods per second) from the producer whose output side it starts
-/// at, or else from the conveyor ending there (followed back up to 12 belts);
-/// () when nothing feeds it.
+/// What reaches conveyor o at its start: #{ rate, item, running, from, ph }
+/// (rate in goods per second; ph: seconds into the loop at which goods land,
+/// so a belt after a robot arm runs in step with it) from the producer whose
+/// output side it starts at, a robot arm putting goods on it, or else the
+/// conveyor ending there (followed back up to 12 belts and arms); () when
+/// nothing feeds it.
 fn conveyor_feed(o, hops) {
     if hops > 12 { return (); }
     let p = o.p;
@@ -78,10 +82,19 @@ fn conveyor_feed(o, hops) {
     for m in objects_at(["producer"], a[0], a[1]) {
         if (m.z - o.z).abs() > 0.5 { continue; }
         if local_of(m, a[0], a[1])[0] > m.p.w / 2.0 - 1.0 {
-            return #{ rate: m.p.rate / 60.0, item: m.p.product, running: m.p.running, from: m.id };
+            return #{ rate: m.p.rate / 60.0, item: m.p.product, running: m.p.running, from: m.id, ph: 0.0 };
         }
     }
     let s = world_of(o, -p.w / 2.0, 0.0);
+    for m in objects_of("robot_arm") {
+        let dx = m.x - s[0];
+        let dy = m.y - s[1];
+        if dx * dx + dy * dy > (m.p.reach + 1.0) * (m.p.reach + 1.0) { continue; }
+        let t = arm_targets(m, hops + 1);
+        if t.put.belt == o.id {
+            return #{ rate: 1.0 / t.cycle, item: t.kind, running: t.running, from: m.id, ph: t.ph + t.cycle * 9.0 / 16.0 };
+        }
+    }
     let zs = o.z + belt_z(p, -p.w / 2.0);
     for c in objects_of("conveyor") {
         if c.id == o.id { continue; }
@@ -91,9 +104,9 @@ fn conveyor_feed(o, hops) {
         if (c.z + belt_z(c.p, c.p.w / 2.0) - zs).abs() > 0.3 { continue; }
         let f = conveyor_feed(c, hops + 1);
         if type_of(f) == "map" {
-            return #{ rate: f.rate, item: f.item, running: f.running && c.p.running, from: c.id };
+            return #{ rate: f.rate, item: f.item, running: f.running && c.p.running, from: c.id, ph: f.ph };
         }
-        return #{ rate: c.p.speed / c.p.gap, item: c.p.item, running: c.p.running, from: c.id };
+        return #{ rate: c.p.speed / c.p.gap, item: c.p.item, running: c.p.running, from: c.id, ph: 0.0 };
     }
     ()
 }
@@ -173,11 +186,15 @@ fn prefab_conveyor(o) {
             if moving {
                 let per = step / p.speed;
                 let v = dv(step, 0.0, p.rise * step / p.w);
-                s.begin("a ride", `--dx:${v[0]}px;--dy:${v[1]}px;animation-duration:${per}s`);
+                // the loop starts when goods land (ph seconds in)
+                let ph = if fed { feed.ph } else { 0.0 };
+                let late = ((per - ph) % per + per) % per;
+                let at = `animation-duration:${per}s;animation-delay:-${late}s`;
+                s.begin("a ride", `--dx:${v[0]}px;--dy:${v[1]}px;${at}`);
                 for i in order {
                     let u = u0 + i * step;
                     let fade = if cnt == 1 { "rideio" } else if i == 0 { "ridein" } else if i == cnt - 1 { "rideout" } else { "" };
-                    if fade != "" { s.begin("a " + fade, `animation-duration:${per}s`); }
+                    if fade != "" { s.begin("a " + fade, at); }
                     s.goods(kind, u, 0.0, belt_z(p, u) + lift, k);
                     if fade != "" { s.end(); }
                 }
@@ -251,3 +268,192 @@ fn prefab_producer(o) {
     s.box(cx, -D, L, D, ct, p.h, mat);
     s.cyl(px, 0.0, 0.2, p.h, p.h + stroke + 0.15, "press");
 }
+
+// ---------------------------------------------------------- robot arms
+
+fn v3(a, b, k) { [a[0] + b[0] * k, a[1] + b[1] * k, a[2] + b[2] * k] }
+/// Angle (radians) of the local plan point (x, y) seen from the origin.
+fn plan_angle(x, y) {
+    let r = (x * x + y * y).sqrt();
+    if r < 1e-9 { return 0.0; }
+    let a = clamp(x / r, -1.0, 1.0).acos();
+    if y < 0.0 { -a } else { a }
+}
+
+fn side_angle(side) {
+    if side == "+y" { PI() / 2.0 } else if side == "-x" { PI() } else if side == "-y" { -PI() / 2.0 } else { 0.0 }
+}
+
+/// Where robot arm o picks and puts goods: #{ pick, put } each #{ r, a, z,
+/// belt } (distance, angle and height in o's frame; the belt id or ""), the
+/// kind of goods, its cycle (s: Cycle, else one per item coming in) and
+/// whether it runs (it waits while the line before it stands).
+fn arm_targets(o, hops) {
+    let p = o.p;
+    let pick = ();
+    let put = ();
+    let kind = "carton";
+    let rate = 0.0;
+    let fed = true;
+    let ph = 0.0;
+    let best = 1e9;
+    if p.pick == "auto" {
+        for c in objects_of("conveyor") {
+            let e = world_of(c, c.p.w / 2.0 - 0.35, 0.0);
+            let l = local_of(o, e[0], e[1]);
+            let d = (l[0] * l[0] + l[1] * l[1]).sqrt();
+            if d < 0.6 || d > p.reach + 0.4 || d >= best { continue; }
+            best = d;
+            pick = #{ r: d, a: plan_angle(l[0], l[1]), z: c.z + belt_z(c.p, c.p.w / 2.0) - o.z, belt: c.id };
+            let f = if hops > 12 { () } else { conveyor_feed(c, hops + 1) };
+            if type_of(f) == "map" { kind = f.item; rate = f.rate; fed = f.running && c.p.running; ph = f.ph; } else { kind = c.p.item; rate = c.p.speed / c.p.gap; fed = c.p.running; ph = 0.0; }
+        }
+    }
+    if type_of(pick) != "map" {
+        let side = if p.pick == "auto" { "-x" } else { p.pick };
+        pick = #{ r: p.reach * 0.75, a: side_angle(side), z: 0.8, belt: "" };
+        kind = p.goods;
+    }
+    if kind == "none" { kind = p.goods; }
+    best = 1e9;
+    if p.put == "auto" {
+        for c in objects_of("conveyor") {
+            if c.id == pick.belt { continue; }
+            let e = world_of(c, -c.p.w / 2.0 + 0.35, 0.0);
+            let l = local_of(o, e[0], e[1]);
+            let d = (l[0] * l[0] + l[1] * l[1]).sqrt();
+            if d < 0.6 || d > p.reach + 0.4 || d >= best { continue; }
+            best = d;
+            put = #{ r: d, a: plan_angle(l[0], l[1]), z: c.z + belt_z(c.p, -c.p.w / 2.0) - o.z, belt: c.id };
+        }
+    }
+    if type_of(put) != "map" {
+        let a = if p.put == "auto" { pick.a + PI() / 2.0 } else { side_angle(p.put) };
+        put = #{ r: p.reach * 0.75, a: a, z: 0.14, belt: "" };
+    }
+    let cycle = if p.cycle > 0.0 { p.cycle } else if rate > 0.0 { 1.0 / rate } else { 4.0 };
+    #{ pick: pick, put: put, kind: kind, cycle: clamp(cycle, 1.5, 120.0), running: p.running && fed, ph: ph }
+}
+
+/// One pose of the arm (links al long, shoulder 1.2 m up): the gripper's tip
+/// at distance r, angle a, height zt, holding an item of kind unless kind is
+/// "". The parts are drawn outer ones last when the arm points at the viewer.
+fn arm_pose(r, a, zt, kind, k, mat, al) {
+    let zs = 1.2;
+    let a1 = al;
+    let a2 = al;
+    let wr = r;
+    let wz = zt + 0.32;
+    let dz = wz - zs;
+    let d = fmin((wr * wr + dz * dz).sqrt(), a1 + a2 - 0.01);
+    let phi = if d < 1e-6 { 0.0 } else { let q = clamp(wr / d, -1.0, 1.0).acos(); if dz < 0.0 { -q } else { q } };
+    let al = clamp((a1 * a1 + d * d - a2 * a2) / (2.0 * a1 * d), -1.0, 1.0).acos();
+    let sh = phi + al;
+    let er = a1 * sh.cos();
+    let ez = zs + a1 * sh.sin();
+    let ca = a.cos();
+    let sa = a.sin();
+    let n = [-sa, ca, 0.0];
+    let S = [0.0, 0.0, zs];
+    let E = [ca * er, sa * er, ez];
+    let W = [ca * wr, sa * wr, wz];
+    let T = [ca * wr, sa * wr, zt];
+    let parts = [0, 1, 2];
+    if !vis(ca, sa) { parts.reverse(); }
+    for part in parts {
+        if part == 0 {
+            this.beam(S, E, n, 0.26, mat);
+            this.beam(v3(E, n, -0.17), v3(E, n, 0.17), [ca, sa, 0.0], 0.3, "robotb");
+        } else if part == 1 {
+            this.beam(E, W, n, 0.2, mat);
+        } else {
+            if kind != "" { this.goods(kind, T[0], T[1], zt - goods_h(kind) * k, k); }
+            this.beam(W, T, n, 0.12, "robotb");
+            this.beam(v3(T, n, -0.16), v3(T, n, 0.16), [ca, sa, 0.0], 0.07, "grip");
+        }
+    }
+    this
+}
+
+fn meta_robot_arm() {
+    #{ label: "Robot arm", category: "Industry", icon: "⟟",
+       help: "Picks goods off the end of the nearest conveyor in its reach and puts them on the start of another one, or on a pallet beside it (Pick from / Put on: auto, or a side of the arm). With Cycle 0 it keeps pace with the goods.",
+       props: [
+         #{ key: "reach", type: "float", def: 2.0, min: 1.0, max: 4.0, step: 0.1, label: "Reach (m)" },
+         #{ key: "pick", type: "choice", def: "auto", choices: ["auto", "+x", "+y", "-x", "-y"], label: "Pick from" },
+         #{ key: "put", type: "choice", def: "auto", choices: ["auto", "+x", "+y", "-x", "-y"], label: "Put on" },
+         #{ key: "cycle", type: "float", def: 0.0, min: 0.0, max: 60.0, step: 0.5, label: "Cycle (s)" },
+         #{ key: "goods", type: "choice", def: "carton", choices: goods_kinds(), label: "Goods" },
+         #{ key: "running", type: "bool", def: true, label: "Running" },
+         #{ key: "colour", type: "choice", def: "robot", choices: ["robot", "mach2", "mach3", "mach1"], label: "Colour" },
+       ] }
+}
+fn prefab_robot_arm(o) {
+    let p = o.p;
+    let t = arm_targets(o, 0);
+    let run = t.running;
+    let k = 0.9;
+    let gh = goods_h(t.kind) * k;
+    let pk = t.pick;
+    let pt = t.put;
+    if pt.belt == "" { pt.z = 0.14 + gh; }
+    let cycle = t.cycle;
+    let al = (p.reach + 0.6) / 2.0;
+    let da = pt.a - pk.a;
+    while da > PI() { da -= 2.0 * PI(); }
+    while da < -PI() { da += 2.0 * PI(); }
+    let pick_from = if pk.belt == "" { "its " + p.pick + " side" } else { pk.belt };
+    let put_on = if pt.belt == "" { "a pallet" } else { pt.belt };
+    let stopped = if p.running { if run { "" } else { " (waiting: the line before it stands)" } } else { " (stopped)" };
+    info_row("Moves", `${t.kind}s from ${pick_from} to ${put_on}`);
+    info_row("Cycle", `${num1(cycle)} s${stopped}`);
+    // the poses over one cycle: [turn from pick to put (0..1), lift (0..1), holding]
+    let F = [[0.0, 0.0, true], [0.0, 0.5, true], [0.0, 1.0, true], [0.2, 1.0, true],
+             [0.45, 1.0, true], [0.7, 1.0, true], [0.9, 1.0, true], [1.0, 1.0, true],
+             [1.0, 0.4, true], [1.0, 0.0, false], [1.0, 0.6, false], [0.8, 1.0, false],
+             [0.55, 1.0, false], [0.3, 1.0, false], [0.1, 1.0, false], [0.0, 0.5, false]];
+    let N = F.len();
+    let ptx = pt.r * pt.a.cos();
+    let pty = pt.r * pt.a.sin();
+    // poses pointing away from the viewer go behind the base, the others in front
+    let behind = [];
+    let front = [];
+    for i in 0..N {
+        if !run && i != 2 { continue; }
+        let te = F[i][0] * F[i][0] * (3.0 - 2.0 * F[i][0]);
+        let a = pk.a + da * te;
+        if vis(a.cos(), a.sin()) { front.push(i); } else { behind.push(i); }
+    }
+    let s = sprite();
+    // a pallet with a layer of goods where it puts them, when not on a belt
+    if pt.belt == "" {
+        s.box(ptx - 0.6, pty - 0.5, ptx + 0.6, pty + 0.5, 0.0, 0.14, "crate");
+        let layer = [[ptx - 0.3, pty - 0.25], [ptx + 0.3, pty - 0.25], [ptx - 0.3, pty + 0.25], [ptx + 0.3, pty + 0.25]];
+        layer.sort(|a, b| if depth(a[0], a[1]) < depth(b[0], b[1]) { -1 } else { 1 });
+        for q in layer { s.goods(t.kind, q[0], q[1], 0.14, k * 0.85); }
+    }
+    for side in [0, 1] {
+        if side == 1 {
+            s.box(-0.45, -0.45, 0.45, 0.45, 0.0, 0.25, "robotb");
+            s.cyl(0.0, 0.0, 0.33, 0.25, 0.95, p.colour);
+            s.cyl(0.0, 0.0, 0.27, 0.95, 1.2, "robotb");
+        }
+        for i in if side == 0 { behind } else { front } {
+            let f = F[i];
+            let te = f[0] * f[0] * (3.0 - 2.0 * f[0]);
+            let a = pk.a + da * te;
+            let r = pk.r + (pt.r - pk.r) * te;
+            let z = pk.z + (pt.z - pk.z) * te;
+            if run {
+                let cls = if i == 0 { "a flip pose0" } else { "a flip" };
+                // pose 0 (the grip) when the last item on the pick belt goes (t.ph seconds in)
+                let delay = (((N - i) % N) * cycle / N - t.ph % cycle + cycle) % cycle;
+                s.begin(cls, `animation-duration:${cycle}s;animation-delay:-${delay}s`);
+            }
+            // put down on a pallet: the item stays there until the next one comes
+            if !f[2] && pt.belt == "" { s.goods(t.kind, ptx, pty, pt.z - gh, k); }
+            s.arm_pose(r, a, z + gh + f[1] * 0.5, if f[2] { t.kind } else { "" }, k, p.colour, al);
+            if run { s.end(); }
+        }
+    }
+}

docs/ROADMAP.md

@@ -74,7 +74,7 @@ Each phase ends with tests, a Studio/viewer check in Edge, commit and push.
 1. ~~Web performance~~ (done, see below)
 2. ~~Conveyors~~ (done, see below)
 3. ~~Producers with adjustable production speed~~ (done, see below)
-4. Robotic arms
+4. ~~Robotic arms~~ (done, see below)
 5. Rounded streets: curved road segments
 6. Sidewalks along streets
 7. Roundabouts
@@ -103,6 +103,11 @@ height, rise, speed; corners join without overlap). A conveyor starting at a pro
 at another conveyor's end, carries those goods, spaced by speed / rate; tooltips show the numbers.
 `examples/factory`, Factory demo in the web Studio.
 
+Robot arm: picks goods off the end of the nearest belt in its reach and puts them on the start of
+another belt or on a pallet, one move per item (or a set cycle), waiting while the line before it
+stands; the belt after it runs in step. Drawn as a 16-pose flipbook (inverse kinematics, links as
+the new native `beam` primitive) shown by a stepped CSS animation.
+
 ## Phase 2: richer editing
 
 - [x] Interior prefabs (see Build your own house); a building `rooms` prop is still open

docs/SCRIPTING.md

@@ -83,6 +83,7 @@ shaded automatically by face direction.
 | `cyl(cx, cy, r, z0, z1, mat[, opts])`, `frust(cx, cy, r0, r1, z0, z1, mat[, sides[, opts]])` | round things |
 | `slope(x0, x1, y0, y1, za, zb, th, mat)` | ramp / stair flight |
 | `face(pts3, mat[, #{id, two_sided}])` | any planar polygon, shaded and culled by its normal (roof slopes, gables) |
+| `beam(a, b, n, w, mat)` | square bar `w` wide between 3D points a and b, `n` a direction across it (robot arms, trusses) |
 | `poly(polys3, cls[, id])` | 3D polygons as one path (solar modules) |
 | `flat(poly or polys, z, cls[, id])` | flat polygon(s); later ones cut holes |
 | `open(a, b, [[u0, u1, z0, z1], …], cls[, id])` | windows / doors on the face a→b (outward normal on the right) |
@@ -122,8 +123,8 @@ cobble, brick) and the site `wall` use it; `house_wall` has its own version
 
 ## Production lines
 
-`producer` and `conveyor` (stdlib/industry.rhai) work together through the
-document, like house parts:
+`producer`, `conveyor` and `robot_arm` (stdlib/industry.rhai) work together
+through the document, like house parts:
 
 - A producer makes one of its `product` goods every 60 / `rate` seconds (its
   ram goes down once per item) and puts them out on its local +x side.
@@ -140,6 +141,17 @@ document, like house parts:
 - The goods ride a group that moves one gap per loop (`iso-ride`), so their
   drawing order never changes; the first fades in, the last fades out.
   Tooltips show speed, rate and where the goods come from (`info_row`).
+- A robot arm picks goods off the end of the nearest conveyor within `reach`
+  (+0.4 m) and puts them on the start of another conveyor within reach, or on
+  a pallet a quarter turn on (`pick` / `put`: auto or a side of the arm). It
+  makes one move per item coming in (`cycle` 0) or every `cycle` seconds, and
+  waits while the line before it stands. The belt it puts on carries its goods
+  and starts its loop when they land, so arm and belts stay in step.
+- The arm is a flipbook: 16 poses (two-link inverse kinematics, links drawn
+  with `beam`), each shown for a sixteenth of the cycle by a stepped CSS
+  animation (`iso-flip`); a rotation cannot turn a 3D arm in this projection.
+  Poses pointing away from the viewer are drawn before the base, the others
+  after it.
 
 ## House parts
 

examples/factory/isokit.toml

@@ -1,7 +1,8 @@
-# isokit factory demo: producers making goods at a set rate, conveyors carrying them.
+# isokit factory demo: producers making goods at a set rate, conveyors carrying them,
+# robot arms passing them on.
 # Open it with `isokit studio examples/factory`.
 title = "isokit factory"
-note = "Presses make goods at a set rate; conveyors carry them at their own speed, so the gap between the goods follows rate and speed. Tap a press or a belt for its numbers. Drag to pan, Ctrl + wheel or pinch to zoom."
+note = "Presses make goods at a set rate; conveyors carry them at their own speed, so the gap between the goods follows rate and speed; robot arms pass them on. Tap a press, belt or robot for its numbers. Drag to pan, Ctrl + wheel or pinch to zoom."
 default_level = "site"
 default_rotation = 1
 prelude = []

examples/factory/scene.json

@@ -7,20 +7,22 @@
     {"id": "press-a", "type": "producer", "x": -14, "y": -4, "props": {"rate": 20, "product": "carton", "colour": "mach1"}, "name": "Carton press", "tag": "Cartons 20/min"},
     {"id": "belt-a1", "type": "conveyor", "x": -8.4, "y": -4, "rot": 0, "props": {"w": 8}, "name": "Carton belt 1"},
     {"id": "belt-a2", "type": "conveyor", "x": -4.4, "y": -1, "rot": 90, "props": {"w": 6}, "name": "Carton belt 2"},
-    {"id": "belt-a3", "type": "conveyor", "x": -0.4, "y": 2, "rot": 0, "props": {"w": 8, "speed": 0.8}, "name": "Carton belt 3"},
+    {"id": "belt-a3", "type": "conveyor", "x": -1.4, "y": 2, "rot": 0, "props": {"w": 6, "speed": 0.8}, "name": "Carton belt 3"},
+    {"id": "robot-a", "type": "robot_arm", "x": 3.2, "y": 2, "name": "Palletiser", "tag": "Palletiser"},
     {"id": "press-b", "type": "producer", "x": 14, "y": -4, "rot": 180, "props": {"rate": 10, "product": "drum", "colour": "mach2", "d": 2.6}, "name": "Drum filler", "tag": "Drums 10/min"},
     {"id": "belt-b1", "type": "conveyor", "x": 9.4, "y": -4, "rot": 180, "props": {"w": 6, "d": 1.0, "speed": 0.4}, "name": "Drum belt"},
-    {"id": "belt-b2", "type": "conveyor", "x": 6.4, "y": 0, "rot": 90, "props": {"w": 8, "d": 1.0, "speed": 0.4, "rise": 1.4}, "name": "Drum incline"},
+    {"id": "belt-b2", "type": "conveyor", "x": 6.4, "y": -1, "rot": 90, "props": {"w": 6, "d": 1.0, "speed": 0.4, "rise": 0.8}, "name": "Drum incline"},
+    {"id": "robot-b", "type": "robot_arm", "x": 6.4, "y": 3.8, "props": {"reach": 2.4, "colour": "mach2"}, "name": "Loading robot"},
+    {"id": "belt-load", "type": "conveyor", "x": 11.5, "y": 5.2, "rot": 0, "props": {"w": 7, "d": 1.0, "speed": 0.6, "rise": 1.0}, "name": "Loading belt"},
+    {"id": "truck", "type": "truck", "x": 16.6, "y": 5.2, "rot": 90, "props": {"len": 9}, "name": "Truck at the dock"},
     {"id": "press-c", "type": "producer", "x": -14, "y": 6, "props": {"rate": 6, "product": "part", "colour": "mach4", "running": false}, "name": "Parts press", "tag": "Stopped", "info": "Waiting for a tool change"},
     {"id": "belt-c1", "type": "conveyor", "x": -9.9, "y": 6, "rot": 0, "props": {"w": 5}, "name": "Parts belt"},
-    {"id": "belt-load", "type": "conveyor", "x": 6.5, "y": 8.5, "rot": 0, "props": {"w": 7, "item": "sack", "gap": 1.1, "speed": 0.6, "rise": 1.0}, "name": "Loading belt"},
-    {"id": "truck", "type": "truck", "x": 13.2, "y": 8.5, "rot": 90, "props": {"len": 9}, "name": "Truck at the dock"},
     {"id": "office", "type": "shed", "x": -5.5, "y": 9.2, "props": {"w": 6, "d": 3.5, "h": 3}, "name": "Shift office"},
-    {"id": "cont-1", "type": "container", "x": 16.8, "y": 0.2, "rot": 90, "props": {"size": "20ft", "stack": 2}, "name": "Empty drums"},
+    {"id": "cont-1", "type": "container", "x": 12.5, "y": 9.8, "rot": 0, "props": {"size": "20ft", "stack": 2}, "name": "Empty drums"},
     {"id": "cont-2", "type": "container", "x": -16.6, "y": 1.5, "rot": 90, "props": {"size": "20ft", "colour": "truckbox"}, "name": "Carton blanks"},
     {"id": "op-a", "type": "person", "x": -14.2, "y": -6.2},
     {"id": "op-c", "type": "person", "x": -11.8, "y": 7.8, "props": {"cls": "hivis"}},
-    {"id": "op-load", "type": "person", "x": 2.4, "y": 9.6},
+    {"id": "op-load", "type": "person", "x": 10.0, "y": 7.2},
     {"id": "tree-1", "type": "tree", "x": -20, "y": 13},
     {"id": "tree-2", "type": "tree", "x": -15, "y": 14},
     {"id": "tree-3", "type": "tree", "x": 19, "y": 14},

tools/check_studio.py

@@ -379,11 +379,19 @@ with sync_playwright() as p:
     pg.locator('#right input[type="number"][data-prop="rate"]').press("Enter")
     pg.wait_for_timeout(900)
     check("30 cartons a minute, 1 m apart" in rows().get("Carries", ""), "a faster producer packs the belt closer: " + rows().get("Carries", "?"))
+    # a robot arm at the belt's end picks the goods off and stacks them on a pallet, one per item
+    pg.evaluate("__studio.op({op: 'add', type: 'robot_arm', x: 19.2, y: -4.5})")
+    pg.wait_for_timeout(900)
+    rid = doc()["objects"][-1]["id"]
+    rrows = dict(pg.evaluate(f"(__studio.view.info('{rid}') || {{}}).rows || []"))
+    check(rrows.get("Moves") == f"cartons from {cv['id']} to a pallet" and rrows.get("Cycle") == "2 s" and
+          pg.evaluate(f"document.querySelectorAll('.iso-svg [data-obj=\"{rid}\"] .iso-flip').length") == 16,
+          f"a robot arm at the belt's end moves its goods to a pallet in step with them: {rrows}")
     pg.screenshot(path=str(OUT / "studio-conveyor.jpg"), type="jpeg", quality=80)
-    for _ in range(3):
+    for _ in range(4):
         pg.locator("#undo").click()
         pg.wait_for_timeout(500)
-    check(len(doc()["objects"]) == n4, "undo takes the producer and the belt back")
+    check(len(doc()["objects"]) == n4, "undo takes the robot, the producer and the belt back")
     pg.evaluate("__studio.select(null)")
     pg.wait_for_timeout(300)
 

tools/check_web.py

@@ -321,6 +321,9 @@ try:
               f"Factory demo opens a production yard ({nf} objects, goods riding {rides} belts, no warnings)")
         carries = pg.evaluate("() => Object.fromEntries((__studio.view.info('belt-a3') || {rows: []}).rows)['Carries'] || ''")
         check("20 cartons a minute" in carries and "(from belt-a2)" in carries, "goods come down the line: " + carries)
+        loads = pg.evaluate("() => Object.fromEntries((__studio.view.info('belt-load') || {rows: []}).rows)['Carries'] || ''")
+        flips = pg.evaluate("() => document.querySelectorAll('.iso-svg .iso-flip').length")
+        check("(from robot-b)" in loads and flips == 32, f"robot arms pass the goods on ({flips} poses): " + loads)
         shot(pg, "web-factory.jpg")
 
         # ---------------------------------------------------------------- folder project (OPFS stands in for a picked folder)

viewer/isokit-view.css

@@ -122,6 +122,10 @@ html[data-theme=light] .iso-svg .iso-glint { display: inline; }
 .iso-svg .iso-rideout { animation: iso-fadeout 2s linear infinite; }
 .iso-svg .iso-rideio { animation: iso-fadeio 2s linear infinite; }
 .iso-svg .iso-ram { animation: iso-ram 2s ease-in-out infinite; }
+/* robot arms: a flipbook of 16 poses, each shown for a sixteenth of the cycle (delays set the turn);
+   unanimated (reduced motion, ghosted) only the first */
+.iso-svg .iso-flip { visibility: hidden; animation: iso-flip16 4s step-end infinite; }
+.iso-svg .iso-flip.iso-pose0 { visibility: visible; }
 .iso-svg .iso-park { display: none; }
 /* paused off-screen (iso-off), when stopped (iso-still), with animation off and during pan/zoom gestures */
 .iso-off .iso-a, .iso-still .iso-a, .iso-off .iso-drive, .iso-still .iso-drive, .iso-off .iso-ledr, .iso-off .iso-ledo, .iso-still .iso-ledr, .iso-still .iso-ledo,
@@ -142,6 +146,7 @@ html[data-theme=light] .iso-svg .iso-glint { display: inline; }
 @keyframes iso-fadein { 0% { opacity: 0; } 35%, 100% { opacity: 1; } }
 @keyframes iso-fadeout { 0%, 65% { opacity: 1; } 100% { opacity: 0; } }
 @keyframes iso-fadeio { 0%, 100% { opacity: 0; } 30%, 70% { opacity: 1; } }
+@keyframes iso-flip16 { 0% { visibility: visible; } 6.25%, 100% { visibility: hidden; } }
 @keyframes iso-ram { 0%, 20%, 100% { transform: translate(0, 0); } 45%, 55% { transform: translate(var(--dx), var(--dy)); } }
 @keyframes iso-move { from { transform: translate(0, 0); } to { transform: translate(var(--dx), var(--dy)); } }
 @keyframes iso-shuttle {