pschatzmann/Springs.ipynb

## Springs.ipynb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3D Printed Springs in OpenSCAD\n",
    "\n",
    "I needed to generate some Springs in OpenSCAD. \n",
    "\n",
    "To simplify my work I have written a very small library which can generate different basic shapes that can be used as springs. This library is described here in this Blog.\n",
    "\n",
    "The basis of most of the functionality is the need to __draw simple lines__ in the 3D space. To do this, we are using simple spheres to generate vertices/nodes. To draw a line between the two nodes we can just use the hull operation! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SCAD code buffer has been cleared"
     ]
    }
   ],
   "source": [
    "%clear"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 20\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* An edge (or line) between 2 nodes\n",
    "*/\n",
    "module line(start, end, d, fn=4) {\n",
    "  hull() {\n",
    "    node(start,d, fn);\n",
    "    node(end,d, fn);\n",
    "  }      \n",
    "}\n",
    "\n",
    "/**\n",
    "* A single node which is connected by edges\n",
    "*/\n",
    "\n",
    "module node(pos, d, fn=4) {\n",
    "  if (pos[0]!=undef && pos[1] != undef && pos[2] != undef){ \n",
    "    translate(pos) sphere(d=d, $fn = fn);    \n",
    "  }\n",
    "}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we are ready to generate the logic for a simple spring. The x position can be calculated with a cos, the y with a sin from the angle and while we rotate we just increase the z poision:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 43\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* Basic logic for generating a 3d spring\n",
    "*/ \n",
    "\n",
    "module spring(d, dBottom=6, dTop=6, windings=2, height=10, steps=10, wireDiameter=1,fn=10) {\n",
    "    // we use either d or dBottom&dTop\n",
    "    r0 = d != undef ? d/2 : dBottom/2;\n",
    "    r1 = d != undef ?d/2 : dTop/2;\n",
    "    \n",
    "    rx = (r0-r1) / (360.0*windings);    \n",
    "    heightPerDegree = height/windings/360;\n",
    "    \n",
    "    for ( angle = [steps : steps : 360*windings] ){\n",
    "        r = r0 - (angle * rx); \n",
    "        x0=r*cos(angle-steps);\n",
    "        y0=r*sin(angle-steps);\n",
    "        z0=(angle-steps)*heightPerDegree;\n",
    "        x=r*cos(angle);\n",
    "        y=r*sin(angle);\n",
    "        z=angle*heightPerDegree;\n",
    "\n",
    "        line([x0,y0,z0],[x,y,z],d=wireDiameter,fn=fn);        \n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 72 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display spring();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This looks quite good - but we want to add a simple horizontal circle at the top and bottom:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 55\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* 3D Spring with identical diameter at top and bottom. The top and boton might\n",
    "* start with a flat circle\n",
    "*/\n",
    "module spring3D(d=5,windings=3,height=10,flatStart=true,flatEnd=true, wireDiameter=1,  fn=4) {  \n",
    "    spring(d=d, windings=windings,height=height, fn=fn);\n",
    "    \n",
    "    if (flatStart)\n",
    "        spring(dBottom=d,dTop=d,windings=1,height=0, fn=fn);\n",
    "    if (flatEnd)\n",
    "        translate([0,0,height]) spring(dBottom=d,dTop=d, windings=1,height=0, fn=fn);\n",
    "\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 180 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display spring3D();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How here is the challange: The further the 3D printing head moves up along the z axis the more springy and wobbly the whole structure gets and therfore this object can not be printed nicely. \n",
    "\n",
    "I tried to add some support in the slicer software - but this does not work either because it will be impossible to remove the support!\n",
    "\n",
    "So we need to print our own support to stabilize the printed object:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 63\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* Generate Support for the 3D Spring\n",
    "*/\n",
    "module spring3DSupport(d=5,height=10,supportDiameter=0.6, fn=4){\n",
    "    // generate support\n",
    "    dist=(d/2)*cos(0);\n",
    "    translate([0,-dist,0])  cylinder(h=height,d=supportDiameter, $fn=fn);\n",
    "    translate([0,dist,0])  cylinder(h=height,d=supportDiameter, $fn=fn);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 182 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%%display\n",
    "spring3D();\n",
    "spring3DSupport();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2D Springs\n",
    "It should be very easy to print 2D shaped objects that can be used as springs because the objects can lay flat on the print bed.\n",
    "\n",
    "\n",
    "## Torsion Springs\n",
    "A 'torsion spring' or 'clock spring' is very similar to the logic that we have described above - we just do not need to move up along the z axis. \n",
    "\n",
    "So we can just use the same functioinality by just keeping the height=0 while we decease the diameter !\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 73\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* Flat \"clock\" Spring\n",
    "*/\n",
    "module springSpiralTorsion(d=15,innerD=6, windings=5,wireDiameter=0.7,fn=4) {\n",
    "    // outer ring\n",
    "    spring(dBottom=d,dTop=d,windings=1,height=0,wireDiameter=wireDiameter,fn=fn);\n",
    "    // windings\n",
    "    spring(dBottom=d,dTop=innerD,windings=windings,height=0,wireDiameter=wireDiameter,fn=fn);\n",
    "    // inner ring\n",
    "    spring(dBottom=innerD,dTop=innerD,windings=1,height=0,wireDiameter=wireDiameter,fn=fn);\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 252 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display springSpiralTorsion();\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Springs shaped like a Sine Wave\n",
    "\n",
    "It is very easy to generate the following 2D shape using the sine function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 85\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* Flat 2d Spring with a sinusoidal shape\n",
    "*/ \n",
    "module springSine(length=20, width=10, windings=4, steps=10, wireDiameter=0.7, fn=4){\n",
    "    dx = length / (360 * windings);\n",
    "    for(i = [steps : steps : 360 * windings]){\n",
    "        x0 = (i-steps) * dx;\n",
    "        y0 = sin(i-steps) * width/2;\n",
    "        x = i * dx;\n",
    "        y = sin(i) * width/2;        \n",
    "        line([x0,y0,0],[x,y,0],d=wireDiameter,fn=fn);        \n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 144 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display springSine();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Triangular Springs \n",
    "\n",
    "This is just a special case of the functionality defined above. When we generate the vertices only ever 90 degrees we get some simle triangles as a result:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 93\n"
     ]
    }
   ],
   "source": [
    "\n",
    "/**\n",
    "* Flat 2d Spring with a triangular shape\n",
    "*/\n",
    "module springTriangle(length=20, width=10, windings=4, wireDiameter=0.7, fn=4){\n",
    "    // generate poins only every 90 degrees\n",
    "    springSine(length=length,width=width, windings=windings, steps=90, wireDiameter=wireDiameter,fn=fn);\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 16 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display springTriangle();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other 3D Springs\n",
    "## Converting the Sine Spring to 3D\n",
    "In the section above we used our line() module to draw our shapes. But we can replace this by using a cylinder in order to get a configurable z dimension: This shape is very easy to 3D print."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of lines of OpenSCAD code: 115\n"
     ]
    }
   ],
   "source": [
    "/**\n",
    "* An edge (or line) between 2 cylinders\n",
    "*/\n",
    "module line3D(start, end,d=1,h=10, fn=4) {\n",
    "  hull() {\n",
    "    translate(start) cylinder(h=h, d=d, $fn = fn);    \n",
    "    translate(end) cylinder(h=h, d=d, $fn = fn);    \n",
    "  }      \n",
    "}\n",
    "\n",
    "/**\n",
    "* 3d Spring with a sinusoidal shape\n",
    "*/ \n",
    "module springSine3D(length=20, heigth=10, width=10, windings=4, steps=10, wireDiameter=0.7, fn=4){\n",
    "    dx = length / (360 * windings);\n",
    "    for(i = [steps : steps : 360 * windings]){\n",
    "        x0 = (i-steps) * dx;\n",
    "        y0 = sin(i-steps) * width/2;\n",
    "        x = i * dx;\n",
    "        y = sin(i) * width/2;        \n",
    "        line3D([x0,y0,0],[x,y,0],d=wireDiameter,h=heigth, fn=fn);  \n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 144 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "%display springSine3D();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Elliptic Leaf Springs\n",
    "We can use \"hollow\" ellipses as springs:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": []
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling design (CSG Products normalization)...\n",
      "Normalized CSG tree has 2 elements\n"
     ]
    },
    {
     "data": {
      "image/png": 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"
     },
     "metadata": {
      "image/png": {
       "height": 400,
       "width": 600
      }
     },
     "output_type": "display_data",
     "source": "kernel"
    }
   ],
   "source": [
    "// we generate an hollow Ellipse\n",
    "module springLeaf(width=3,len=10,height=5){\n",
    " scale([len/10,height/10,1]) difference() {\n",
    "     cylinder(h=width, r=10, center=true);\n",
    "     cylinder(h=width+2, r=9, center=true);\n",
    "  }\n",
    "}\n",
    "\n",
    "%display springLeaf();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "It is quite easy to define different shapes that can be used as springs in OpenSCAD. \n",
    "We have set the fn parameters quite small in order to increase the rendering speed. It is recommended to increase this value when you generate your final model that is printed. \n",
    "\n",
    "Here is the complete code:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/**\n",
      "* An edge (or line) between 2 nodes\n",
      "*/\n",
      "module line(start, end, d, fn=4) {\n",
      "  hull() {\n",
      "    node(start,d, fn);\n",
      "    node(end,d, fn);\n",
      "  }      \n",
      "}\n",
      "\n",
      "/**\n",
      "* A single node which is connected by edges\n",
      "*/\n",
      "\n",
      "module node(pos, d, fn=4) {\n",
      "  if (pos[0]!=undef && pos[1] != undef && pos[2] != undef){ \n",
      "    translate(pos) sphere(d=d, $fn = fn);    \n",
      "  }\n",
      "}\n",
      "/**\n",
      "* Basic logic for generating a 3d spring\n",
      "*/ \n",
      "\n",
      "module spring(d, dBottom=6, dTop=6, windings=2, height=10, steps=10, wireDiameter=1,fn=10) {\n",
      "    // we use either d or dBottom&dTop\n",
      "    r0 = d != undef ? d/2 : dBottom/2;\n",
      "    r1 = d != undef ?d/2 : dTop/2;\n",
      "    \n",
      "    rx = (r0-r1) / (360.0*windings);    \n",
      "    heightPerDegree = height/windings/360;\n",
      "    \n",
      "    for ( angle = [steps : steps : 360*windings] ){\n",
      "        r = r0 - (angle * rx); \n",
      "        x0=r*cos(angle-steps);\n",
      "        y0=r*sin(angle-steps);\n",
      "        z0=(angle-steps)*heightPerDegree;\n",
      "        x=r*cos(angle);\n",
      "        y=r*sin(angle);\n",
      "        z=angle*heightPerDegree;\n",
      "\n",
      "        line([x0,y0,z0],[x,y,z],d=wireDiameter,fn=fn);        \n",
      "    }\n",
      "}/**\n",
      "* 3D Spring with identical diameter at top and bottom. The top and boton might\n",
      "* start with a flat circle\n",
      "*/\n",
      "module spring3D(d=5,windings=3,height=10,flatStart=true,flatEnd=true, wireDiameter=1,  fn=4) {  \n",
      "    spring(d=d, windings=windings,height=height, fn=fn);\n",
      "    \n",
      "    if (flatStart)\n",
      "        spring(dBottom=d,dTop=d,windings=1,height=0, fn=fn);\n",
      "    if (flatEnd)\n",
      "        translate([0,0,height]) spring(dBottom=d,dTop=d, windings=1,height=0, fn=fn);\n",
      "\n",
      "}/**\n",
      "* Generate Support for the 3D Spring\n",
      "*/\n",
      "module spring3DSupport(d=5,height=10,supportDiameter=0.6, fn=4){\n",
      "    // generate support\n",
      "    dist=(d/2)*cos(0);\n",
      "    translate([0,-dist,0])  cylinder(h=height,d=supportDiameter, $fn=fn);\n",
      "    translate([0,dist,0])  cylinder(h=height,d=supportDiameter, $fn=fn);\n",
      "}/**\n",
      "* Flat \"clock\" Spring\n",
      "*/\n",
      "module springSpiralTorsion(d=15,innerD=6, windings=5,wireDiameter=0.7,fn=4) {\n",
      "    // outer ring\n",
      "    spring(dBottom=d,dTop=d,windings=1,height=0,wireDiameter=wireDiameter,fn=fn);\n",
      "    // windings\n",
      "    spring(dBottom=d,dTop=innerD,windings=windings,height=0,wireDiameter=wireDiameter,fn=fn);\n",
      "    // inner ring\n",
      "    spring(dBottom=innerD,dTop=innerD,windings=1,height=0,wireDiameter=wireDiameter,fn=fn);\n",
      "}/**\n",
      "* Flat 2d Spring with a sinusoidal shape\n",
      "*/ \n",
      "module springSine(length=20, width=10, windings=4, steps=10, wireDiameter=0.7, fn=4){\n",
      "    dx = length / (360 * windings);\n",
      "    for(i = [steps : steps : 360 * windings]){\n",
      "        x0 = (i-steps) * dx;\n",
      "        y0 = sin(i-steps) * width/2;\n",
      "        x = i * dx;\n",
      "        y = sin(i) * width/2;        \n",
      "        line([x0,y0,0],[x,y,0],d=wireDiameter,fn=fn);        \n",
      "    }\n",
      "}\n",
      "/**\n",
      "* Flat 2d Spring with a triangular shape\n",
      "*/\n",
      "module springTriangle(length=20, width=10, windings=4, wireDiameter=0.7, fn=4){\n",
      "    // generate poins only every 90 degrees\n",
      "    springSine(length=length,width=width, windings=windings, steps=90, wireDiameter=wireDiameter,fn=fn);\n",
      "}\n",
      "/**\n",
      "* An edge (or line) between 2 cylinders\n",
      "*/\n",
      "module line3D(start, end,d=1,h=10, fn=4) {\n",
      "  hull() {\n",
      "    translate(start) cylinder(h=h, d=d, $fn = fn);    \n",
      "    translate(end) cylinder(h=h, d=d, $fn = fn);    \n",
      "  }      \n",
      "}\n",
      "\n",
      "/**\n",
      "* 3d Spring with a sinusoidal shape\n",
      "*/ \n",
      "module springSine3D(length=20, heigth=10, width=10, windings=4, steps=10, wireDiameter=0.7, fn=4){\n",
      "    dx = length / (360 * windings);\n",
      "    for(i = [steps : steps : 360 * windings]){\n",
      "        x0 = (i-steps) * dx;\n",
      "        y0 = sin(i-steps) * width/2;\n",
      "        x = i * dx;\n",
      "        y = sin(i) * width/2;        \n",
      "        line3D([x0,y0,0],[x,y,0],d=wireDiameter,h=heigth, fn=fn);  \n",
      "    }\n",
      "}// we generate an hollow Ellipse\n",
      "module springLeaf(width=3,len=10,height=5){\n",
      " scale([len/10,height/10,1]) difference() {\n",
      "     cylinder(h=width, r=10, center=true);\n",
      "     cylinder(h=width+2, r=9, center=true);\n",
      "    }\n",
      "}\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%displayCode"
   ]
  },
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   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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