diff --git a/examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb b/examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb
index 63dda44..148e277 100644
--- a/examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb
+++ b/examples/worm_cutting_tool/cutting_tool_worm_assembly.ipynb
@@ -425,17 +425,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 1,
    "id": "0811a6d6-4544-4a99-b4bd-ba5cf6b9027e",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "PATH_TO_FREECAD_LIBDIR not specified, using default FreeCAD version in /Users/lo/mambaforge/envs/freecad/lib\n"
+     ]
+    },
     {
      "data": {
       "text/plain": [
-       "<Shape object at 0x6000011f2df0>"
+       "<Part::PartFeature>"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 1,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -464,17 +471,18 @@
     "    def z(y, t):\n",
     "        r = length(y)\n",
     "        return - module * num_threads * np.arcsin(x / r) / 2 + r * np.tan(alpha) + t\n",
-    "        # return r * np.tan(alpha) + t\n",
     "    \n",
     "    def dz_dy(y):\n",
     "        r = length(y)\n",
     "        return module * num_threads * x * dlength_dy(y) / \\\n",
     "               (2 * np.sqrt(1 - x ** 2 / r ** 2 ) * r ** 2) + \\\n",
     "               np.tan(alpha) * dlength_dy(y)\n",
-    "        # return np.tan(alpha) * dlength_dy(y)\n",
     "        \n",
     "    def distance_yp(y, t):\n",
     "        return np.sqrt((y_p - y) ** 2 + z(y, t) ** 2)\n",
+    "\n",
+    "    def distance_yp_2(y, t):\n",
+    "        return (y_p - y) ** 2 + z(y, t) ** 2\n",
     "    \n",
     "    def ddistance_yp_dy(y, t):\n",
     "        return (y - y_p + z(y, t) * dz_dy(y)) / distance_yp(y, t)\n",
@@ -489,7 +497,7 @@
     "\n",
     "    def min_head(pars):\n",
     "        y, t = pars\n",
-    "        r_0 = y_p -  2 * module # * (1 + clearence)\n",
+    "        r_0 = y_p -  5 * module # * (1 + clearence)\n",
     "        # y_inner = r_0 * np.cos(np.arcsin(x / r_0))\n",
     "        return ddistance_yp_dy(y, t) ** 2 + (y - r_0) ** 2\n",
     "\n",
@@ -526,37 +534,45 @@
     "            T = np.linalg.inv(T_2 @ T_1 @ T_0)\n",
     "            \n",
     "            # find point on curve for given t\n",
-    "            y = sp.optimize.minimize(distance_yp, y_p, (t)).x[0]\n",
+    "            y = sp.optimize.root(ddistance_yp_dy, y_p, (t)).x[0]\n",
     "            z_i = z(y, t) #  - y_p * np.tan(alpha) + np.sign(alpha) * module * np.pi / 4\n",
     "            point = np.array([x, y, z_i, 1.])\n",
     "            xyz_section.append((T @ point)[:3])\n",
     "        xyz.append(np.array(xyz_section))\n",
     "\n",
     "    return np.array(xyz)\n",
+    "\n",
+    "# parameters\n",
+    "module = 1.\n",
+    "teeth = 50\n",
+    "height = 5\n",
+    "worm_pitch_diameter = 10\n",
+    "num_threads = 1\n",
+    "alpha = np.deg2rad(20)\n",
+    "y_p = worm_pitch_diameter / 2\n",
+    "r_w = teeth * module / 2\n",
+    "clearence = 0.25\n",
+    "head = 0.\n",
     "    \n",
     "# create two surfaces one for positive alpha and one for negative alpha\n",
-    "\n",
-    "for alpha in [np.deg2rad(- 20), np.deg2rad(20)]:   \n",
+    "for alpha_i in [-alpha, alpha]:   \n",
     "    curves = []\n",
-    "    for line in compute_involute(alpha=alpha).transpose(1, 0, 2):\n",
+    "    xyz = compute_involute(\n",
+    "        module=module,\n",
+    "        teeth=teeth, \n",
+    "        height=height,\n",
+    "        worm_pitch_diameter=worm_pitch_diameter,\n",
+    "        num_threads=num_threads,\n",
+    "        alpha=alpha_i)\n",
+    "    \n",
+    "    for line in xyz.transpose(1, 0, 2):\n",
     "        bs = part.BSplineCurve()\n",
     "        points = [app.Vector(*point) for point in line]\n",
     "        bs.interpolate(points)\n",
     "        curves.append(bs.toShape())\n",
     "    part.show(part.makeLoft(curves))\n",
     "\n",
-    "# create cutting survaces for head and bottom\n",
-    "# 1. compute strat and end of phi\n",
-    "\n",
-    "height = 5\n",
-    "worm_pitch_diameter = 10\n",
-    "teeth = 15\n",
-    "y_p = worm_pitch_diameter / 2\n",
-    "r_w = 7.5\n",
-    "module = 1.\n",
-    "clearence = 0.25\n",
-    "head = 0.\n",
-    "\n",
+    "# create cutting surfaces for head and bottom\n",
     "r_head = y_p - module * (1 + head)\n",
     "r_foot = y_p + module * (1 + clearence)\n",
     "\n",
@@ -593,31 +609,6 @@
     "part.show(part.makeLoft(curves_head))"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "id": "5737ef53-ab3c-4ea4-98e7-09cfc111f956",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Help on function numeric_transformation in module pygears.transformation:\n",
-      "\n",
-      "numeric_transformation(angle, axis, translation=array([0., 0., 0.]))\n",
-      "    see http://en.wikipedia.org/wiki/SO%284%29#The_Euler.E2.80.93Rodrigues_formula_for_3D_rotations\n",
-      "    angle: angle of rotation\n",
-      "    axis: the axis of the rotation\n",
-      "    translation: translation of transformation\n",
-      "\n"
-     ]
-    }
-   ],
-   "source": [
-    "help(numeric_transformation)"
-   ]
-  },
   {
    "cell_type": "code",
    "execution_count": null,