diff --git a/files.html b/files.html
index 1c1157d1386c0343af3b7b689a2b7758bab76d74..792ef7417003487f4eac291c10718ac532ea58fb 100644
--- a/files.html
+++ b/files.html
@@ -67,6 +67,7 @@
<a href='./modules/frep/shapes/2D/circle'>circle</a><br>
<a href='./modules/frep/shapes/2D/function'>function</a><br>
<a href='./modules/frep/shapes/2D/involute%20gear'>involute gear</a><br>
+ <a href='./modules/frep/shapes/2D/involute%20rack'>involute rack</a><br>
<a href='./modules/frep/shapes/2D/polygon'>polygon</a><br>
<a href='./modules/frep/shapes/2D/rectangle'>rectangle</a><br>
<a href='./modules/frep/shapes/2D/right%20triangle'>right triangle</a><br>
diff --git a/modules/frep/shapes/2D/involute rack b/modules/frep/shapes/2D/involute rack
new file mode 100644
index 0000000000000000000000000000000000000000..093b3f1ed2a4d1577af9aea3f0e25960c9525f47
--- /dev/null
+++ b/modules/frep/shapes/2D/involute rack
@@ -0,0 +1,193 @@
+//
+// frep involute gear
+//
+// Neil Gershenfeld
+// (c) Massachusetts Institute of Technology 2018
+//
+// This work may be reproduced, modified, distributed, performed, and
+// displayed for any purpose, but must acknowledge the mods
+// project. Copyright is retained and must be preserved. The work is
+// provided as is; no warranty is provided, and users accept all
+// liability.
+//
+// closure
+//
+(function(){
+//
+// module globals
+//
+var mod = {}
+//
+// name
+//
+var name = 'frep involute gear'
+//
+// initialization
+//
+var init = function() {
+ mod.module.value = '1'
+ mod.angle.value = '20'
+ mod.teeth.value = '10'
+ }
+//
+// inputs
+//
+var inputs = {
+ variables:{type:'',
+ event:function(evt){
+ for (var p in evt.detail)
+ mod[p].value = evt.detail[p]
+ outputs.variables.event()
+ outputs.shape.event()
+ }}}
+//
+// outputs
+//
+var outputs = {
+ shape:{type:'',
+ event:function(){
+ var module = parseFloat(mod.module.value)
+ var angle = Math.PI*parseFloat(mod.angle.value)/180
+ var teeth = parseFloat(mod.teeth.value)
+ //
+ // pitch radius
+ //
+ var rp = module*teeth/2
+ mod.info.innerHTML = `pitch radius: ${rp.toFixed(3)} mm<br>`
+ //
+ // base radius
+ //
+ var rb = rp*Math.cos(angle)
+ mod.info.innerHTML += `base radius: ${rb.toFixed(3)} mm<br>`
+ //
+ // addendum height
+ //
+ var ha = 1.0*module
+ mod.info.innerHTML += `outer radius: ${(rp+ha).toFixed(3)} mm<br>`
+ //
+ // dedendum height
+ //
+ var hd = 1.1*module
+ mod.info.innerHTML += `root radius: ${(rp-hd).toFixed(3)} mm<br>`
+ //
+ // involute angle
+ //
+ var ai = Math.tan(angle)-angle
+ mod.info.innerHTML += `inv angle: ${(ai*180/Math.PI).toFixed(3)} deg<br>`
+ //
+ // pitch angle
+ //
+ var ap = 2*Math.PI/teeth
+ mod.info.innerHTML += `pitch angle: ${(ap*180/Math.PI).toFixed(3)} deg<br>`
+ //
+ // shapes
+ //
+ // must be inside tip
+ //
+ var fn = `${rp}+${ha}-Math.sqrt(X*X+Y*Y)`
+ //
+ // angle must be above bottom involute
+ //
+ var fn = `Math.min(${fn},(Math.PI+Math.atan2(Y,X))%${ap}-(Math.sqrt(Math.pow(Math.max(${rb},Math.sqrt(X*X+Y*Y))/${rb},2)-1)-Math.acos(${rb}/Math.max(${rb},Math.sqrt(X*X+Y*Y)))))`
+ //
+ // angle must be below top involute
+ //
+ var fn = `Math.min(${fn},-(Math.sqrt(Math.pow(Math.max(${rb},Math.sqrt(X*X+Y*Y))/${rb},2)-1)-Math.acos(${rb}/Math.max(${rb},Math.sqrt(X*X+Y*Y))))-(-${ap/2+2*ai}+(Math.PI+Math.atan2(Y,X))%${ap}))`
+ //
+ // root circle
+ //
+ var fn = `Math.max(${fn},${rp-hd}-Math.sqrt(X*X+Y*Y))`
+ //
+ // todo: fillets
+ //
+ // output
+ //
+ var variables = ['X','Y']
+ var limits = [[-rp-ha,+rp+ha],[-rp-ha,+rp+ha]]
+ var type = 'Magnitude'
+ var shape = {function:fn,variables:variables,limits:limits,type:type}
+ mods.output(mod,'shape',shape)}},
+
+/*
+angle = +-(sqrt((r/rb)^2 - 1) - acos(rb/r)) (r > rb)
+(x % n + n) % n
+*/
+
+ variables:{type:'',
+ event:function(){
+ var module = parseFloat(mod.module.value)
+ var angle = parseFloat(mod.angle.value)
+ var teeth = parseFloat(mod.teeth.value)
+ var vars = {module:module,angle:angle,teeth:teeth}
+ mods.output(mod,'variables',vars)}
+ }}
+//
+// interface
+//
+var interface = function(div){
+ mod.div = div
+ //
+ // module
+ //
+ div.appendChild(document.createTextNode('module (mm): '))
+ var input = document.createElement('input')
+ input.type = 'text'
+ input.size = 3
+ div.appendChild(input)
+ mod.module = input
+ div.appendChild(document.createElement('br'))
+ //
+ // angle
+ //
+ div.appendChild(document.createTextNode('pressure angle: '))
+ var input = document.createElement('input')
+ input.type = 'text'
+ input.size = 3
+ div.appendChild(input)
+ mod.angle = input
+ div.appendChild(document.createElement('br'))
+ //
+ // teeth
+ //
+ div.appendChild(document.createTextNode('number of teeth: '))
+ var input = document.createElement('input')
+ input.type = 'text'
+ input.size = 3
+ div.appendChild(input)
+ mod.teeth = input
+ div.appendChild(document.createElement('br'))
+ //
+ // info
+ //
+ var info = document.createElement('span')
+ div.appendChild(info)
+ mod.info = info
+ //
+ // output button
+ //
+ var btn = document.createElement('button')
+ btn.style.padding = mods.ui.padding
+ btn.style.margin = 1
+ btn.appendChild(document.createTextNode('output'))
+ btn.addEventListener('click',function(){
+ outputs.variables.event()
+ outputs.shape.event()
+ })
+ div.appendChild(btn)
+ }
+//
+// local functions
+//
+;
+//
+// return values
+//
+return ({
+ mod:mod,
+ name:name,
+ init:init,
+ inputs:inputs,
+ outputs:outputs,
+ interface:interface
+ })
+}())
diff --git a/modules/index.js b/modules/index.js
index 42083bc04eb997ea624c5283a51dc54b4d08b02f..70a483c6e8229869459e73c359754071d6f2361a 100644
--- a/modules/index.js
+++ b/modules/index.js
@@ -38,6 +38,7 @@ module_menu(' arc','modules/frep/shapes/2D/arc')
module_menu(' circle','modules/frep/shapes/2D/circle')
module_menu(' function','modules/frep/shapes/2D/function')
module_menu(' involute gear','modules/frep/shapes/2D/involute%20gear')
+module_menu(' involute rack','modules/frep/shapes/2D/involute%20rack')
module_menu(' polygon','modules/frep/shapes/2D/polygon')
module_menu(' rectangle','modules/frep/shapes/2D/rectangle')
module_menu(' right triangle','modules/frep/shapes/2D/right%20triangle')