OpenSCAD "unknown variable sin/cos" on lines 166,167

// New Geared Rail Design
// aka 2020 rack + carriage
// + "top" facing rack (mates to underside of carriage)
// + 2x "outside" facing racks (mate to "insides" of carriage)
// + Gears inside carriage (underside and insides)
// + Compresive-tension / placement screws for matched gears (anti-backlash mechanism) (springs necessary?)
// + Fasten-and-fit carriage body for ease of assembly / capture

// Author: S.J.Gilpin


// Thanks go to teepee from the OpenSCAD IRC community for their assistance below


include <sjgilpin/2020profiles.scad>;

length = 40;


#translate ([0,10,-10]) rotate ([0,90,0]) linear_extrude (length+20) 2020tslot (width=20,height=20,cut=([1,2,3,4]));

//translate ([10,0,0]) cube ([length,20,20]);
translate ([10,0,0]) 2020rackrail(length=length);
translate ([0,40,0]) 2020rack_carriage();



module 2020rackrail (length=30) {
    // outline as polygon extrudable profile for outside racks, cut round holes from main block every 50 mm
        // correction: holes every (1.5707963 * 20 = 31.415926)mm, and (1.5376771 * 8 = 12.5663704)mm from the ends)
    // outline as separate polygon extrudable profile for top rack, predesign round holes from teeth every 50 mm
        // See hole spacing correction above
    // try to keep it basic for now, get fancy with stuff like herringbone much later
    // extend far end of polygon profile beyond rack profile where length exceeds multiples of 8th decimal of pi

    //sideracks_whole();
    linear_extrude (12.7) sideracks_whole();
    translate ([0,20,12.7]) {
        toprack_whole();
    };

    module sideracks_whole () {
        tiproot_south = [[0,0], [0.3315616,0], [0.6182283,0.6], [0.7960060,1], [1.3020953,2.138701], [1.3265373,2.161097], [1.3528373,2.181278], [1.3807963,2.19909], [1.4102013,2.214397], [1.4408283,2.227083], [1.4724451,2.237052], [1.50481,2.244227], [1.5376771,2.248554]]; // 13p
        roottip_south = [[0,2.25], [0.0331192,2.248554], [0.0659863,2.244227], [0.0983512,2.237052], [0.129968,2.227083], [0.160595,2.214397], [0.19,2.19909], [0.217959,2.181278], [0.244259,2.161097], [0.268701,2.138701], [0.7747903,1], [0.9525680,0.6], [1.2392347,0]]; // 13p
        rt_south_last = [[0,2.25], [0.0331192,2.248554], [0.0659863,2.244227], [0.0983512,2.237052], [0.129968,2.227083], [0.160595,2.214397], [0.19,2.19909], [0.217959,2.181278], [0.244259,2.161097], [0.268701,2.138701], [0.7747903,1], [0.952680,0.6], [1.2392347,0], [1.5707963,0]]; // 14p
        tiproot_north = [[0,2.25], [0.3315616,2.25], [0.6182283,1.65], [0.7960060,1.25], [1.3020953,0.111299], [1.3265373,0.088903], [1.3528373,0.068722], [1.3807963,0.05091], [1.4102013,0.035603], [1.4408283,0.022917], [1.4724451,0.012948], [1.50481,0.005773], [1.5376771,0.001446]]; // 13p
        roottip_north = [[0,0], [0.0331192,0.001446], [0.0659863,0.005773], [0.0983512,0.012948], [0.129968,0.022917], [0.160595,0.035603], [0.19,0.05091], [0.217959,0.068722], [0.244259,0.088903], [0.268701,0.111299], [0.7747903,1.25], [0.952680,1.65], [1.2392347,2.25]];
        rt_north_last = [[0,0], [0.0331192,0.001446], [0.0659863,0.005773], [0.0983512,0.012948], [0.129968,0.022917], [0.160595,0.035603], [0.19,0.05091], [0.217959,0.068722], [0.244259,0.088903], [0.268701,0.111299], [0.7747903,1.25], [0.952680,1.65], [1.2392347,2.25], [1.5707963,2.25]]; // 14p

        toothcount = floor(length/(1.5707963*2));
        echo("Tooth Count is:",toothcount);
        pathlen = 2*(toothcount*26)+8;

        swcorner = [0,2.6];
        secutin = [toothcount*(1.5707963*2),2.6];
        secorner = [length,2.6];
        necorner = [length,17.4];
        necutin = [toothcount*(1.5707963*2),17.4];
        nwcorner = [0,17.4];

        cut_tooth_south = [each [for (i=[0:12]) tiproot_south[i], for (i=[0:12]) [roottip_south[i][0]+1.5707963,roottip_south[i][1]]]];
        ct_south_last = [each [for (i=[0:12]) tiproot_south[i],for (i=[0:13]) [rt_south_last[i][0]+1.5707963,rt_south_last[i][1]]]];
        cut_rack_south = [each [for (a=[0:toothcount-2],b=[0:25]) [cut_tooth_south[b][0]+((1.5707963*2)*a),cut_tooth_south[b][1]],for (i=[0:26]) [ct_south_last[i][0]+((1.5707963*2)*(toothcount-1)),ct_south_last[i][1]]]];
        cut_tooth_north = [each [for (i=[12:-1:0]) roottip_north[i], for (i=[12:-1:0]) [tiproot_north[i][0]-1.5707963,tiproot_north[i][1]]]];
        ct_north_last = [each [for (i=[13:-1:0]) rt_north_last[i], for (i=[12:-1:0]) [tiproot_north[i][0]-1.5707963,tiproot_north[i][1]]]];
        cut_rack_north = [each [for (i=[0:26]) [ct_north_last[i][0]+((toothcount-0.5)*(1.5707963*2)),ct_north_last[i][1]+17.75],for (a=[1:toothcount-1],b=[0:25]) [cut_tooth_north[b][0]-((1.5707963*2)*a)+((toothcount-0.5)*(1.5707963*2)),cut_tooth_north[b][1]+17.75]]];
        southlen = len(cut_rack_south);
        northlen = len(cut_rack_north);

        bore_angle = [for (i=[0:19]) [2.55*cos(i*(360/20)),2.55*sin(i*(360/20))]]; // 9 mm hole
        borecount = floor((length-(1.5707963*20))/(1.5707963*20)+2);
        bore_xposition = [for (a=[0:borecount-1]) (a == 0) ? 12.5663704 : (a == (borecount-1)) ? (length-12.5663704) : 15.707963+(31.415926*a)];
        cut_bore_points = [for (a=[0:borecount-1],b=[0:19]) [bore_angle[b][0]+bore_xposition[a],bore_angle[b][1]+10]];
        bore_pathlen = 20*borecount;

        outerpath = [for (i=[0:pathlen-1]) i];
        borepath = [for (a=[0:borecount-1]) [for (b=[0:19]) pathlen+(a*20)+b]];

        //echo ("north tooth contains",cut_tooth_north);
        //echo ("north last contains",ct_north_last);
        //echo ("north rack contains",cut_rack_north);
        //echo ("bore_angle[i][0]",[for (i=[0:19]) bore_angle[i][0]]);
        //echo ("bore points contains",cut_bore_points);
        //echo ("bore angle contains",bore_angle);
        //echo ("bore x positions are",bore_xposition);
        //echo ("bore count is",borecount);
        //echo(pathlen);
        //echo("borepath contains",borepath);

        polygon (
            points = [
                swcorner,
                for (i=[0:southlen-1]) cut_rack_south[i],
                secutin,
                secorner,
                necorner,
                necutin,
                for (i=[0:northlen-1]) cut_rack_north[i],
                nwcorner,
                for (i=[0:bore_pathlen-1]) cut_bore_points[i]
            ],
            paths = [
                outerpath,(each[for (i=[borecount-1:-1:0]) borepath[i]])
            ]
        );


    };

    module toprack_whole () {
        tiproot = [[0,2.35], [0.3315616,2.35], [0.6182283,1.75], [0.7960060,1.35], [1.3020953,0.211299], [1.3265373,0.188903], [1.3528373,0.168722], [1.3807963,0.15091], [1.4102013,0.135603], [1.4408283,0.122917], [1.4724451,0.112948], [1.50481,0.105773], [1.5376771,0.101446]];
        roottip = [[0,0.1], [0.0331192,0.101446], [0.0659863,0.105773], [0.0983512,0.112948], [0.129968,0.122917], [0.160595,0.135603], [0.19,0.15091], [0.217959,0.168722], [0.244259,0.188903], [0.268701,0.211299], [0.7747903,1.35], [0.952680,1.75], [1.2392347,2.35]];
        roottip_last = [[0,0.1], [0.0331192,0.101446], [0.0659863,0.105773], [0.0983512,0.112948], [0.129968,0.122917], [0.160595,0.135603], [0.19,0.15091], [0.217959,0.168722], [0.244259,0.188903], [0.268701,0.211299], [0.7747903,1.35], [0.952680,1.75], [1.2392347,2.35], [1.5707963,2.35]];

        toothcount = floor(length/(1.5707963*2));
        pathlen = (toothcount*26)+3;
        swcorner = [0,0];
        secorner = [toothcount*(1.5707963*2),0];

        cut_tooth = [each [for (i=[0:12]) tiproot[i], for (i=[0:12]) [roottip[i][0]+1.5707963,roottip[i][1]]]];
        cut_tooth_last = [each [for (i=[0:12]) tiproot[i], for (i=[0:13]) [roottip_last[i][0]+1.5707963,roottip_last[i][1]]]];
        cut_rack = [each [for (a=[0:toothcount-2],b=[0:25]) [cut_tooth[b][0]+((1.5707963*2)*a),cut_tooth[b][1]+4.95],for (i=[0:26]) [cut_tooth_last[i][0]+((1.5707963*2)*(toothcount-1)),cut_tooth_last[i][1]+4.95]]];

        borecount = floor((length-(1.5707963*20))/(1.5707963*20)+2);
        bore_xposition = [for (a=[0:borecount-1]) (a == 0) ? 12.5663704 : (a == (borecount-1)) ? (length-12.5663704) : 15.707963+(31.415926*a)];

        outerpath = [for (i=[0:pathlen-1]) i];

        difference() {
            rotate ([90,0,0]) linear_extrude (20) polygon (
                points = [
                    swcorner,
                    for (i=[0:pathlen-3]) cut_rack[i],
                    secorner
                ]
            );
        for (a=[0:borecount-1]) translate ([bore_xposition[a],-10,-1]) cylinder (h=10,r=4.5);
        };

        //translate ([12.5663704,-10,-2.25]) color ("green") cylinder (h=5,d=8.72);
    };
};

module 2020rack_carriage () {
    // multiple parts to easily assemble for gear housing purpose
    // one stationary gear and one adjustable gear per sub-rack to allow anti-backlash pre-tension
    // four surface-mounting holes centered 32 mm from eachother on y and 36 to 50 mm on x

    mod1gear();

    module mod1gear () {
        tiproot = [[0,2.35], [0.3315616,2.35], [0.6182283,1.75], [0.7960060,1.35], [1.3020953,0.211299], [1.3265373,0.188903], [1.3528373,0.168722], [1.3807963,0.15091], [1.4102013,0.135603], [1.4408283,0.122917], [1.4724451,0.112948], [1.50481,0.105773], [1.5376771,0.101446]];
        roottip = [[0,0.1], [0.0331192,0.101446], [0.0659863,0.105773], [0.0983512,0.112948], [0.129968,0.122917], [0.160595,0.135603], [0.19,0.15091], [0.217959,0.168722], [0.244259,0.188903], [0.268701,0.211299], [0.7747903,1.35], [0.952680,1.75], [1.2392347,2.35]];

        pitch_radius = 10;
        circumference = 2*3.1415926*pitch_radius;
        if ((circumference / 3.1415926) != (floor(circumference / 3.1415926))) {
            echo ("The gear is sized improperly for the tooth size. It currently fits",(circumference/3.1415926),"teeth.");
            echo ("For more teeth, consider changing the radius to",(ceil(circumference / 3.1415926)/2));
            echo ("Or for less teeth, consider",(floor(circumference / 3.1415926)/2));
        };
        tooth_count = circumference / 3.1415926;
        pathlen = tooth_count*26;

        cut_tooth = [each [for (i=[0:12]) tiproot[i], for (i=[0:12]) [roottip[i][0]+1.5707963,roottip[i][1]]]];
        //tooth_angle = [each [for (a=[0:tooth_count-1],b=[0:25]) [cut_tooth[b][0]+(pitch_radius*cos*(a*b*(360/pathlen))),cut_tooth[b][1]+(pitch_radius*sin*(a*b*(360/pathlen)))]]];
        tooth_angle = [each [for (a=[0:tooth_count-1],b=[0:25]) [(cut_tooth[b][0]+pitch_radius)*cos*(a*b*(360/pathlen)),(cut_tooth[b][1]+pitch_radius)*sin*(a*b*(360/pathlen))]]];



    };


};





//linear_extrude (20) 2020tslot(width=40,height=40,cut=[1,2,3,4,5,6,7,8,9,10]);





/* Rack Tooth Form Notes

module = 1.0
add. = 1.0
ded. = 1.25
pitch = pi x mod (3.1415926) OR (3.1415927)
thick = pitch/2 (1.5707963)
dist = pitch/2 (1.5707963)
rootrad = 0.38 (measured WHERE? negMod?) (ends -45~45?)
fillet height = max 0.6
fillet width = max 0.02
pa = 20 deg = 4/9 = 0.44 repeating


central dedendum 1 = 0,0
pitch = pi (3.1415926) OR (3.1415927)
thick&dist = pi/2 (1.5707963)
central addendum 1 = (pi/2,2.25) (1.5707963,2.25)


root wedge:
= 0deg [0,-0.38]
= 5    [0.0331192,-0.0378554] // WRONG [0.0331192,-0.378554]
= 10   [0.0659863,-0.374227]
= 15   [0.0983512,-0.367052]
= 20   [0.129968,-0.357083]
= 25   [0.160595,-0.344397]
= 30   [0.19,-0.32909]
= 35   [0.217959,-0.311278]
= 40   [0.244259,-0.291097]
= 45   [0.268701,-0.268701]

root wedge global:
= 0deg [0,0]
= 5    [0.0331192,0.3421446] // WRONG [0.0331192,0.001446]
= 10   [0.0659863,0.005773]
= 15   [0.0983512,0.012948]
= 20   [0.129968,0.022917]
= 25   [0.160595,0.035603]
= 30   [0.19,0.05091]
= 35   [0.217959,0.068722]
= 40   [0.244259,0.088903]
= 45   [0.268701,0.111299]


tooth edge node at pitch line = (+0.55,+1.25)xModule above inters. pa&ded.
inters. of pa&add. = (+1,+2.25)xModule avove inters. pa&ded.
    pa&ded = (0.21923477777777777777777777777778,0) shortened to (0.2192347,0) OR (0.2192348,0)
    pa&pitch = (0.7747902,1.25) OR (0.7747902,1.25)
    pa&add = (1.2192347,2.25) OR (1.2192348,2.25)


tip fillet y = 1.65 = (0.952681,1.65)
tip fillet x = 1.23.... = (1.2392347,2.25)


root to tip:
= 0deg [0,0]
= 5    [0.0331192,0.3421446] // WRONG, see above ([0.0331192,0.001446])
= 10   [0.0659863,0.005773]
= 15   [0.0983512,0.012948]
= 20   [0.129968,0.022917]
= 25   [0.160595,0.035603]
= 30   [0.19,0.05091]
= 35   [0.217959,0.068722]
= 40   [0.244259,0.088903]
= 45   [0.268701,0.111299]
= pa&p [0.2192347,1.25] // WRONG, see below ([0.7747903,1.25])
= fily [0.952681,1.65] // WRONG, see below ([0.9525680,1.65])
= filx [1.2392347,2.25]
= tip  [1.5707963,2.25]

root to tip (incl., 14p):
[0,0], [0.0331192,0.001446], [0.0659863,0.005773], [0.0983512,0.012948], [0.129968,0.022917], [0.160595,0.035603], [0.19,0.05091], [0.217959,0.068722], [0.244259,0.088903], [0.268701,0.111299], [0.7747903,1.25], [0.952680,1.65], [1.2392347,2.25], [1.5707963,2.25]

root to tip (excl., 13p):
[0,0], [0.0331192,0.001446], [0.0659863,0.005773], [0.0983512,0.012948], [0.129968,0.022917], [0.160595,0.035603], [0.19,0.05091], [0.217959,0.068722], [0.244259,0.088903], [0.268701,0.111299], [0.7747903,1.25], [0.952680,1.65], [1.2392347,2.25]

pa&p = intersection of pressure angle and pitch line
fily = tip fillet on y axis
filx = tip fillet on x axis
tip = tip center of tooth

tip to root:
= tip  [0,2.25]
= filx [0.3315616,2.25]
= fily [0.6181153,1.65] // WRONG, correct it ([0.6182283,1.65])
= pa&p [1.3515616,1.25] // WRONG, correct it ([0.7960060,1.25])
= 45   [1.3020953,0.111299]
= 40   [1.3265373,0.088903]
= 35   [1.3528373,0.068722]
= 30   [1.3807963,0.05091]
= 25   [1.4102013,0.035603]
= 20   [1.4408283,0.022917]
= 15   [1.4724451,0.012948]
= 10   [1.50481,0.005773]
= 5    [1.5376771,0.3421446] // WRONG ([1.5376771,0.001446])
= 0deg [1.5707963,0]

tip to root (incl.):
[0,2.25], [0.3315616,2.25], [0.6182283,1.65], [0.7960060,1.25], [1.3020953,0.111299], [1.3265373,0.088903], [1.3528373,0.068722], [1.3807963,0.05091], [1.4102013,0.035603], [1.4408283,0.022917], [1.4724451,0.012948], [1.50481,0.005773], [1.5376771,0.001446], [1.5707963,0]

tip to root (excl.):
[0,2.25], [0.3315616,2.25], [0.6182283,1.65], [0.7960060,1.25], [1.3020953,0.111299], [1.3265373,0.088903], [1.3528373,0.068722], [1.3807963,0.05091], [1.4102013,0.035603], [1.4408283,0.022917], [1.4724451,0.012948], [1.50481,0.005773], [1.5376771,0.001446]



root to tip, inverted y:
= 0deg [0,2.25]
= 5    [0.0331192,1.9078554] // 2.248554
= 10   [0.0659863,2.244227]
= 15   [0.0983512,2.237052]
= 20   [0.129968,2.227083]
= 25   [0.160595,2.214397]
= 30   [0.19,2.19909]
= 35   [0.217959,2.181278]
= 40   [0.244259,2.161097]
= 45   [0.268701,2.138701]
= pa&p [0.2192347,1] // 0.7747903,1
= fily [0.952681,0.6] // 0.9525680,0.6
= filx [1.2392347,0]
= tip  [1.5707963,0]

root to tip, inverted y (incl.):
[0,2.25], [0.0331192,2.248554], [0.0659863,2.244227], [0.0983512,2.237052], [0.129968,2.227083], [0.160595,2.214397], [0.19,2.19909], [0.217959,2.181278], [0.244259,2.161097], [0.268701,2.138701], [0.7747903,1], [0.952680,0.6], [1.2392347,0], [1.5707963,0]

root to tip, inverted y (excl.):
[0,2.25], [0.0331192,2.248554], [0.0659863,2.244227], [0.0983512,2.237052], [0.129968,2.227083], [0.160595,2.214397], [0.19,2.19909], [0.217959,2.181278], [0.244259,2.161097], [0.268701,2.138701], [0.7747903,1], [0.952680,0.6], [1.2392347,0]

tip to root, inverted y:
= tip  [0,0]
= filx [0.3315616,0]
= fily [0.6181153,0.6] // 0.6182283,0.6
= pa&p [1.3515616,1] // 0.7960060,1
= 45   [1.3020953,2.138701]
= 40   [1.3265373,2.161097]
= 35   [1.3528373,2.181278]
= 30   [1.3807963,2.19909]
= 25   [1.4102013,2.214397]
= 20   [1.4408283,2.227083]
= 15   [1.4724451,2.237052]
= 10   [1.50481,2.244227]
= 5    [1.5376771,1.9078554] // 2.248554
= 0deg [1.5707963,2.25]

tip to root, inverted y (incl.):
[0,0], [0.3315616,0], [0.6182283,0.6], [0.7960060,1], [1.3020953,2.138701], [1.3265373,2.161097], [1.3528373,2.181278], [1.3807963,2.19909], [1.4102013,2.214397], [1.4408283,2.227083], [1.4724451,2.237052], [1.50481,2.244227], [1.5376771,2.248554], [1.5707963,2.25]

tip to root, inverted y (excl.):
[0,0], [0.3315616,0], [0.6182283,0.6], [0.7960060,1], [1.3020953,2.138701], [1.3265373,2.161097], [1.3528373,2.181278], [1.3807963,2.19909], [1.4102013,2.214397], [1.4408283,2.227083], [1.4724451,2.237052], [1.50481,2.244227], [1.5376771,2.248554]


Corrected data from above
y-y1 = m (x-x1)
m=(y-y1)/(x-x1)
the y-intercept of the equation of a line in the point-slope form is: (0, y₁ - mx₁) or y₁ - mx₁
y=mx+b (y=[slope]x+[y0])
=9x-4y=1.9731128 OR 1.9731132
y=mx+c (y=[slope]x+[x0])
y0=-0.4932782 OR -0.4932783
x0=0.2192347 OR 0.2192348
slope (m) of 2.25 (20deg from vertical)

[0.268701,0.111299] (45deg point 0.38 radius from 0,0)

[0.7747903,1.25] OR [0.7747904,1.25]

[0.9525680,1.65] OR [0.9525681,1.65]

[1.2192347,2.25] OR [1.2192348,2.25]
([1.2392347,2.25] OR [1.2392347,2.25])



*/