Summary

OpenSCAD source code

/*
OpenSCAD code for centiped walking model

To animate in OpenSCAD, go to View -> Animate. In the animation fields,
set FPS to 3 and Steps to a value between 20-50.

The purpose of this script is to visualize the motion of a centipede's
legs in both modes of locomotion: with leg waves propagating from back
to front, and front to back -- with both modes resulting in forward
movement of the centipede.

Each segment of the centipede has a pair of legs that constantly windmill
around. Each successive segment has the phase of the windmilling offset
by 45 degrees from the previous segment. The offset direction is
controlled by the 'phase_direction' parameter. The phase_direction
values 1 or -1 result in forward or backward propagation, respectively.

The legs flex at the knees to look more natural.
*/

// ---------- customizable values ----------

phase_direction = 1;    // Set to 1 (back-to-front waves) or -1

segspacing = 12;    // spacing between segments
nsegs = 21;         // number of segments
leglen = 22;        // leg length at max extension
legr = 2;           // leg radius
legkneeht = 3;      // knee height at max leg extension
legangle = 15;      // overal downward leg tilt angle from body

// ---------- calculated values ----------

bodywid = 1.5*segspacing;           // body segment width
body_elev = leglen*sin(legangle);   // elevation of bottom of body above floor
legseglen = sqrt(leglen*leglen*0.25 + legkneeht*legkneeht); // length of a leg segment (each leg is 2 segments)
xmotion = 1.7*segspacing;           // front-to-back motion of each foot in the x direction
llmin = leglen*cos(asin(0.5*xmotion/leglen));   // minimum leg length when leg is perpendicular to body and foot is on the floor

// --------- render ----------

// $t is set internally by the animation option; initially it is zero.
// It ranges from 0 to 1 in increments determined by Steps, and repeats.

centipede(360*$t);
floor(360*$t);

// ---------- modules ----------

// render the whole centipede
module centipede(phase=0) {
    ns2 = nsegs/2;
    for(i=[0:nsegs-1]) translate([segspacing*(i-ns2),0,0]) bodyseg(phase, phase_direction*i*45);
    translate([segspacing*(-1-ns2),0,0]) head();
}

// single body segment with legs positioned at phase angle 'phase' with phase offset 'offset'
module bodyseg(phase=0, offset=0) {
    bodyblank();
    translate([0,0,body_elev]) color("orange") {
        translate([0,bodywid,legr]) rotate([-legangle,0,0]) leg(phase, offset);
        mirror([0,1,0]) translate([0,bodywid,legr]) rotate([-legangle,0,0]) leg(phase+180, offset);
    }
}

// head includes eyes and antennae, but no legs
module head() {
    bodyblank();
    // eyes
    translate([-bodywid/3,bodywid/2,body_elev+bodywid/3]) color("#00FF00") sphere(r=bodywid/4, $fn=20);
    translate([-bodywid/3,-bodywid/2,body_elev+bodywid/3]) color("#00FF00") sphere(r=bodywid/4, $fn=20);
    // antennae
    rotate([20,0,-45]) translate([0,0,body_elev+1]) color("brown") cylinder(bodywid*1.3, r=legr/2, $fn=8);
    rotate([-20,0,45]) translate([0,0,body_elev+1]) color("brown") cylinder(bodywid*1.3, r=legr/2, $fn=8);
}

// blank body segment, used by bodyseg() and head()
module bodyblank() {
    translate([0,0,body_elev])
        color("gray") scale([0.618,1,1]) {
            cylinder(2*legr, r=bodywid, $fn=24);
            translate([0,0,2*legr]) scale([1,1,0.382]) sphere(r=bodywid, $fn=24);
        }
}

// Model of one leg.
// The 'foot' of the leg follows a straight line backward on the floor, and arches
// over forward in a semicircle. The knee flexes to accommodate moving backward in
// a straight line, with full extension in the forward and back positions.
module leg(phase=0, offset=0) {
    ph = (phase + offset + 3600) % 360;
    if (ph < 180) {
        x = 0.5*xmotion*cos(ph);
        y = 0.5*xmotion*sin(ph);
        zrot = -asin(x/leglen);
        xrot = asin(y/leglen);
        rotate([0,0,zrot]) rotate([xrot,0,0]) ballcylinder([0,0,0], [0,leglen/2,legkneeht], [0,leglen,0]);
    } else {
        x = xmotion * ((ph-180)/180 - 0.5);
        zrot = -asin(x/leglen);
        ll = sqrt(llmin*llmin + x*x);
        kneeht = sqrt(legseglen*legseglen - ll*ll*0.25);
        
        rotate([0,0,zrot]) ballcylinder([0,0,0], [0,ll/2,kneeht], [0,ll,0]);
    }
}

// the leg is two segments with a knee; parameters are coordinates of the root, knee, and foot.
module ballcylinder(p1, p2, p3, r=legr) {
    fn = 10;
    hull() {
        translate(p1) sphere(r=r, $fn=fn);
        translate(p2) sphere(r=r, $fn=fn);
    }
    hull() {
        translate(p2) sphere(r=r, $fn=fn);
        translate(p3) sphere(r=r, $fn=fn);
    }        
}

// moving floor tiles
module floor(phase=0) {
    xp = phase/360 * 2*xmotion;
    for(i=[0:nsegs+6]) let(x=(i-nsegs/2-3)*xmotion)
        for(j=[0:10]) let(y=(j-5)*xmotion, col = (i+j)%2==0 ? "white":"lightblue")
            translate([x+xp,y,0]) color(col) cube([xmotion,xmotion,0.1], center=true);
}

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