Add rack to mesh with involute spur gears.

Added a utility for making involute spur gears
Added degrees, radians and rot2_z() to maths.scad.
2025-09-03 20:32:35 +02:00 · 2020-07-07 22:36:34 +01:00 · 2020-07-06 23:22:11 +01:00 · 2020-07-06 12:43:24 +01:00 · 2020-07-04 17:30:26 +01:00 · 2020-07-04 14:57:01 +01:00
18 changed files with 360 additions and 73 deletions
--- a/lib.scad
+++ b/lib.scad
@@ -29,6 +29,7 @@ include <vitamins/batteries.scad>
 include <vitamins/blowers.scad>
 include <vitamins/bulldogs.scad>
 include <vitamins/buttons.scad>
+include <vitamins/cameras.scad>
 include <vitamins/components.scad>
 include <vitamins/displays.scad>
 include <vitamins/extrusions.scad>
@@ -83,6 +84,7 @@ use <utils/rounded_cylinder.scad>
 use <utils/dogbones.scad>
 use <utils/tube.scad>
 use <utils/quadrant.scad>
+use <utils/gears.scad>
 use <utils/hanging_hole.scad>
 use <utils/fillet.scad>
 use <utils/rounded_polygon.scad>
--- a/libtest.png
+++ b/libtest.png
--- a/libtest.scad
+++ b/libtest.scad
@@ -385,7 +385,7 @@ sk_brackets_y = extrusion_brackets_y + 80;
 kp_pillow_blocks_y = sk_brackets_y + 50;
 scs_bearing_blocks_y = kp_pillow_blocks_y + 60;

-translate([x4 + 150, belts_y + 58]) {
+translate([x4 + 200, belts_y + 58]) {
    belt_test();

    translate([0, 60])
--- a/readme.md
+++ b/readme.md
@@ -22,19 +22,19 @@ See [usage](docs/usage.md) for requirements, installation instructions and a usa
 <tr><td> <a href = "#Ball_bearings">Ball_bearings</a> </td><td> <a href = "#KP_pillow_blocks">KP_pillow_blocks</a> </td><td> <a href = "#Ring_terminals">Ring_terminals</a> </td><td> <a href = "#Butt_box">Butt_box</a> </td><td> <a href = "#Bezier">Bezier</a> </td><td> <a href = "#Clip">Clip</a> </td></tr>
 <tr><td> <a href = "#Batteries">Batteries</a> </td><td> <a href = "#LDRs">LDRs</a> </td><td> <a href = "#Rockers">Rockers</a> </td><td> <a href = "#Cable_grommets">Cable_grommets</a> </td><td> <a href = "#Dogbones">Dogbones</a> </td><td> <a href = "#Global">Global</a> </td></tr>
 <tr><td> <a href = "#Belts">Belts</a> </td><td> <a href = "#LED_meters">LED_meters</a> </td><td> <a href = "#Rod">Rod</a> </td><td> <a href = "#Carriers">Carriers</a> </td><td> <a href = "#Fillet">Fillet</a> </td><td> <a href = "#Polyholes">Polyholes</a> </td></tr>
-<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
-<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Layout">Layout</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
-<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Maths">Maths</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
-<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
-<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
-<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
-<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
-<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
-<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
-<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
-<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
-<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
-<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td></td><td></td></tr>
+<tr><td> <a href = "#Blowers">Blowers</a> </td><td> <a href = "#LEDs">LEDs</a> </td><td> <a href = "#SCS_bearing_blocks">SCS_bearing_blocks</a> </td><td> <a href = "#Corner_block">Corner_block</a> </td><td> <a href = "#Gears">Gears</a> </td><td> <a href = "#Rounded_rectangle">Rounded_rectangle</a> </td></tr>
+<tr><td> <a href = "#Bulldogs">Bulldogs</a> </td><td> <a href = "#Leadnuts">Leadnuts</a> </td><td> <a href = "#SK_brackets">SK_brackets</a> </td><td> <a href = "#Door_hinge">Door_hinge</a> </td><td> <a href = "#Hanging_hole">Hanging_hole</a> </td><td> <a href = "#Sphere">Sphere</a> </td></tr>
+<tr><td> <a href = "#Buttons">Buttons</a> </td><td> <a href = "#Light_strips">Light_strips</a> </td><td> <a href = "#SMDs">SMDs</a> </td><td> <a href = "#Door_latch">Door_latch</a> </td><td> <a href = "#Layout">Layout</a> </td><td> <a href = "#Teardrops">Teardrops</a> </td></tr>
+<tr><td> <a href = "#Cable_strips">Cable_strips</a> </td><td> <a href = "#Linear_bearings">Linear_bearings</a> </td><td> <a href = "#SSRs">SSRs</a> </td><td> <a href = "#Fan_guard">Fan_guard</a> </td><td> <a href = "#Maths">Maths</a> </td><td></td></tr>
+<tr><td> <a href = "#Cameras">Cameras</a> </td><td> <a href = "#Mains_sockets">Mains_sockets</a> </td><td> <a href = "#Screws">Screws</a> </td><td> <a href = "#Fixing_block">Fixing_block</a> </td><td> <a href = "#Offset">Offset</a> </td><td></td></tr>
+<tr><td> <a href = "#Circlips">Circlips</a> </td><td> <a href = "#Microswitches">Microswitches</a> </td><td> <a href = "#Sealing_strip">Sealing_strip</a> </td><td> <a href = "#Flat_hinge">Flat_hinge</a> </td><td> <a href = "#Quadrant">Quadrant</a> </td><td></td></tr>
+<tr><td> <a href = "#Components">Components</a> </td><td> <a href = "#Microview">Microview</a> </td><td> <a href = "#Sheets">Sheets</a> </td><td> <a href = "#Foot">Foot</a> </td><td> <a href = "#Round">Round</a> </td><td></td></tr>
+<tr><td> <a href = "#DIP">DIP</a> </td><td> <a href = "#Modules">Modules</a> </td><td> <a href = "#Spades">Spades</a> </td><td> <a href = "#Handle">Handle</a> </td><td> <a href = "#Rounded_cylinder">Rounded_cylinder</a> </td><td></td></tr>
+<tr><td> <a href = "#D_connectors">D_connectors</a> </td><td> <a href = "#Nuts">Nuts</a> </td><td> <a href = "#Spools">Spools</a> </td><td> <a href = "#PCB_mount">PCB_mount</a> </td><td> <a href = "#Rounded_polygon">Rounded_polygon</a> </td><td></td></tr>
+<tr><td> <a href = "#Displays">Displays</a> </td><td> <a href = "#O_ring">O_ring</a> </td><td> <a href = "#Springs">Springs</a> </td><td> <a href = "#PSU_shroud">PSU_shroud</a> </td><td> <a href = "#Sector">Sector</a> </td><td></td></tr>
+<tr><td> <a href = "#Extrusion_brackets">Extrusion_brackets</a> </td><td> <a href = "#Opengrab">Opengrab</a> </td><td> <a href = "#Stepper_motors">Stepper_motors</a> </td><td> <a href = "#Printed_box">Printed_box</a> </td><td> <a href = "#Sweep">Sweep</a> </td><td></td></tr>
+<tr><td> <a href = "#Extrusions">Extrusions</a> </td><td> <a href = "#PCB">PCB</a> </td><td> <a href = "#Swiss_clips">Swiss_clips</a> </td><td> <a href = "#Ribbon_clamp">Ribbon_clamp</a> </td><td> <a href = "#Thread">Thread</a> </td><td></td></tr>
+<tr><td> <a href = "#Fans">Fans</a> </td><td> <a href = "#PCBs">PCBs</a> </td><td> <a href = "#Toggles">Toggles</a> </td><td> <a href = "#SSR_shroud">SSR_shroud</a> </td><td> <a href = "#Tube">Tube</a> </td><td></td></tr>
 <tr><td> <a href = "#Fuseholder">Fuseholder</a> </td><td> <a href = "#PSUs">PSUs</a> </td><td> <a href = "#Transformers">Transformers</a> </td><td> <a href = "#Screw_knob">Screw_knob</a> </td><td></td><td></td></tr>
 <tr><td> <a href = "#Geared_steppers">Geared_steppers</a> </td><td> <a href = "#Panel_meters">Panel_meters</a> </td><td> <a href = "#Tubings">Tubings</a> </td><td> <a href = "#Socket_box">Socket_box</a> </td><td></td><td></td></tr>
 <tr><td> <a href = "#Green_terminals">Green_terminals</a> </td><td> <a href = "#Pillars">Pillars</a> </td><td> <a href = "#Variacs">Variacs</a> </td><td> <a href = "#Strap_handle">Strap_handle</a> </td><td></td><td></td></tr>
@@ -133,7 +133,8 @@ Also single bearing balls are modelled as just a silver sphere and a BOM entry.
 |   1 | ```ball_bearing(BB6201)``` |  Ball bearing 6201-2RS 12mm x 32mm x 10mm |
 |   1 | ```ball_bearing(BB624)``` |  Ball bearing 624-2RS 4mm x 13mm x 5mm |
 |   1 | ```ball_bearing(BB6808)``` |  Ball bearing 6808-2RS 40mm x 52mm x 7mm |
-|   5 | ``` bearing_ball(3)``` |  Steel ball 3mm |
+|   1 | ```ball_bearing(BBSMR95)``` |  Ball bearing SMR95ZZ 5mm x 9mm x 2.5mm |
+|   6 | ``` bearing_ball(3)``` |  Steel ball 3mm |


 <a href="#top">Top</a>
@@ -447,7 +448,8 @@ PCB cameras.
 ### Properties
 | Function | Description |
 |:--- |:--- |
-| ```camera_connector(type)``` | The flex connector block for the camera itself |
+| ```camera_connector_pos(type)``` | The flex connector block for the camera itself's position |
+| ```camera_connector_size(type)``` | The flex connector block for the camera itself's size |
 | ```camera_lens(type)``` | Stack of lens parts, can be round, rectanular or rounded rectangular, with optional tapered aperture |
 | ```camera_lens_offset(type)``` | Offset of the lens center from the PCB centre |
 | ```camera_pcb(type)``` | The PCB part of the camera |
@@ -456,6 +458,7 @@ PCB cameras.
 | Module | Description |
 |:--- |:--- |
 | ```camera(type)``` | Draw specified PCB camera |
+| ```camera_lens(type, offset = 0)``` | Draw the lens stack, with optional offset for making a clearance hole |

 ![cameras](tests/png/cameras.png)

@@ -463,6 +466,7 @@ PCB cameras.
 | Qty | Module call | BOM entry |
 | ---:|:--- |:---|
 |   1 | ```camera(rpi_camera_v1)``` |  Raspberry Pi camera V1 |
+|   1 | ```camera(rpi_camera_v2)``` |  Raspberry Pi camera V2 |
 |   1 | ```camera(rpi_camera)``` |  Raspberry Pi focusable camera |


@@ -2103,6 +2107,7 @@ PCBs and perfboard with optional components. The shape can be a rectangle with o
 | ```pcb_coord(type, p)``` | Convert offsets from the edge to coordinates relative to the centre |
 | ```pcb_grid_pos(type, x, y, z = 0)``` | Returns a pcb grid position |
 | ```pcb_screw(type, cap = hs_cap)``` | Mounting screw type |
+| ```pcb_size(type)``` | Length, width and thickness in a vector |

 ### Modules
 | Module | Description |
@@ -2235,6 +2240,7 @@ PCBs and perfboard with optional components. The shape can be a rectangle with o
 | ```pcb_coord(type, p)``` | Convert offsets from the edge to coordinates relative to the centre |
 | ```pcb_grid_pos(type, x, y, z = 0)``` | Returns a pcb grid position |
 | ```pcb_screw(type, cap = hs_cap)``` | Mounting screw type |
+| ```pcb_size(type)``` | Length, width and thickness in a vector |

 ### Modules
 | Module | Description |
@@ -2652,24 +2658,27 @@ Linear rails with carriages.
 ### Vitamins
 | Qty | Module call | BOM entry |
 | ---:|:--- |:---|
-|   1 | ```rail(MGN15, 260)``` |  Linear rail MGN15 x 260mm |
+|   1 | ```rail(MGN12, 200)``` |  Linear rail MGN12 x 200mm |
+|   1 | ```rail(MGN12H, 200)``` |  Linear rail MGN12H x 200mm |
+|   1 | ```rail(MGN15, 200)``` |  Linear rail MGN15 x 200mm |
 |   1 | ```rail(MGN5, 200)``` |  Linear rail MGN5 x 200mm |
 |   1 | ```rail(MGN7, 200)``` |  Linear rail MGN7 x 200mm |
 |   1 | ```rail(MGN9, 200)``` |  Linear rail MGN9 x 200mm |
 |   1 | ```rail(SSR15, 200)``` |  Linear rail SSR15 x 200mm |
 |  26 | ```nut(M2_nut, nyloc = true)``` |  Nut M2 x 1.6mm nyloc |
-|  17 | ```nut(M3_nut, nyloc = true)``` |  Nut M3 x 2.4mm nyloc |
+|  31 | ```nut(M3_nut, nyloc = true)``` |  Nut M3 x 2.4mm nyloc |
 |   4 | ```nut(M4_nut, nyloc = true)``` |  Nut M4 x 3.2mm nyloc |
 |  11 | ```screw(M2_cap_screw, 10)``` |  Screw M2 cap x 10mm |
 |  15 | ```screw(M2_cs_cap_screw, 10)``` |  Screw M2 cs cap x 10mm |
 |   8 | ```screw(M3_cap_screw, 10)``` |  Screw M3 cap x 10mm |
-|   5 | ```screw(M3_cap_screw, 16)``` |  Screw M3 cap x 16mm |
+|  12 | ```screw(M3_cap_screw, 12)``` |  Screw M3 cap x 12mm |
+|   3 | ```screw(M3_cap_screw, 16)``` |  Screw M3 cap x 16mm |
 |   2 | ```screw(M3_cs_cap_screw, 12)``` |  Screw M3 cs cap x 12mm |
-|   2 | ```screw(M3_cs_cap_screw, 16)``` |  Screw M3 cs cap x 16mm |
+|   6 | ```screw(M3_cs_cap_screw, 16)``` |  Screw M3 cs cap x 16mm |
 |   2 | ```screw(M4_cap_screw, 16)``` |  Screw M4 cap x 16mm |
 |   2 | ```screw(M4_cs_cap_screw, 20)``` |  Screw M4 cs cap x 20mm |
 |  26 | ```washer(M2_washer)``` |  Washer  M2 x 5mm x 0.3mm |
-|  17 | ```washer(M3_washer)``` |  Washer  M3 x 7mm x 0.5mm |
+|  31 | ```washer(M3_washer)``` |  Washer  M3 x 7mm x 0.5mm |
 |   4 | ```washer(M4_washer)``` |  Washer  M4 x 9mm x 0.8mm |


@@ -5212,6 +5221,47 @@ Rounded fillet for adding to corners.
 ![fillet](tests/png/fillet.png)


+<a href="#top">Top</a>
+
+---
+<a name="Gears"></a>
+## Gears
+Utilities for making involute gears.
+
+Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
+and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
+
+```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
+Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
+
+Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
+the practical minimum.
+
+The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
+
+The origin of the rack is the left end of the pitch line and its width is below the pitch line. I.e. it does not include the addendum.
+
+
+[utils/gears.scad](utils/gears.scad) Implementation.
+
+[tests/gears.scad](tests/gears.scad) Code for this example.
+
+### Functions
+| Function | Description |
+|:--- |:--- |
+| ```centre_distance(m, z1, z2, pa)``` | Calculate distance between centres taking profile shift into account |
+| ```involute(r, u)``` | Involute of circle radius r at angle u in radians |
+| ```profile_shift(z, pa)``` | Calculate profile shift for small gears |
+
+### Modules
+| Module | Description |
+|:--- |:--- |
+| ```involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20)``` | Calculate gear profile given module, number of teeth and pressure angle |
+| ```involute_rack_profile(m, z, w, pa = 20, clearance = undef)``` | Calculate rack profile given module, number of teeth and pressure angle |
+
+![gears](tests/png/gears.png)
+
+
 <a href="#top">Top</a>

 ---
@@ -5274,17 +5324,21 @@ Maths utilities for manipulating vectors and matrices.
 |:--- |:--- |
 | ```angle_between(v1, v2)``` | Return the angle between two vectors |
 | ```augment(m)``` | Augment a matrix by adding an identity matrix to the right |
+| ```degrees(radians)``` | Convert degrees to radians |
 | ```euler(R)``` | Convert a rotation matrix to a Euler rotation vector. |
 | ```identity(n, x = 1)``` | Construct an arbitrary size identity matrix |
 | ```invert(m)``` | Invert a matrix |
 | ```nearly_zero(x)``` | True if x is close to zero |
+| ```radians(degrees)``` | Convert radians to degrees |
 | ```reverse(v)``` | Reverse a vector |
+| ```rot2_z(a)``` | Generate a 2x2 matrix to rotate around z |
 | ```rot3_z(a)``` | Generate a 3x3 matrix to rotate around z |
 | ```rotate(a, v)``` | Generate a 4x4 rotation matrix, ```a``` can be a vector of three angles or a single angle around ```z```, or around axis ```v``` |
 | ```rowswap(m, i, j)``` | Swap two rows of a matrix |
 | ```scale(v)``` |  Generate a 4x4 matrix that scales by ```v```, which can be a vector of xyz factors or a scalar to scale all axes equally |
 | ```solve(m, i = 0, j = 0)``` | Solve each row ensuring diagonal is not zero |
 | ```solve_row(m, i)``` | Make diagonal one by dividing the row by it and subtract from other rows to make column zero |
+| ```sqr(x)``` | Square x |
 | ```transform(v, m)``` | Apply 4x4 transform to a 3 vector by extending it and cropping it again |
 | ```transform_points(path, m)``` | Apply transform to a path |
 | ```translate(v)``` | Generate a 4x4 translation matrix, ```v``` can be ```[x, y]```, ```[x, y, z]``` or ```z``` |
--- a/tests/gears.scad
+++ b/tests/gears.scad
@@ -0,0 +1,66 @@
+//
+// NopSCADlib Copyright Chris Palmer 2020
+// nop.head@gmail.com
+// hydraraptor.blogspot.com
+//
+// This file is part of NopSCADlib.
+//
+// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
+// GNU General Public License as published by the Free Software Foundation, either version 3 of
+// the License, or (at your option) any later version.
+//
+// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
+// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+// See the GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along with NopSCADlib.
+// If not, see <https://www.gnu.org/licenses/>.
+//
+include <../utils/core/core.scad>
+use <../utils/gears.scad>
+
+// left gear teeth
+z1 = 39; // [7 : 1 : 99]
+
+// Right gear teeth
+z2 = 7; // [7 : 1 : 99]
+
+//  Modulus
+m = 2.0; // [0.1 : 0.1 : 5.0]
+
+// Pressure angle
+pa = 20; // [14.5, 20, 22.5, 25]
+
+$show_numbers = false;
+
+module gears() {
+    color(pp1_colour)
+        rotate(-$t * 360)
+            linear_extrude(eps, center = true, convexity = z1)
+                difference() {
+                    involute_gear_profile(m, z1, pa);
+
+                    circle(r = m * z1 / 10);
+                }
+
+    color(pp2_colour)
+        translate([centre_distance(m, z1, z2, pa), 0])
+            rotate(180 + 180 / z2 + $t * 360 * z1 / z2)
+               linear_extrude(eps, center = true, convexity = z2)
+                    difference() {
+                         involute_gear_profile(m, z2, pa);
+
+                         circle(r = m * z2 / 10);
+                    }
+
+    z3 = floor((z1 + z2) / PI);
+    angle = -$t * 360 + 90 - floor(z1 / 4) * 360 / z1; // Line up the rack 1/4 turn around the gear
+    pitch = m * PI;
+    color(pp3_colour)
+        translate([(angle % ((z3 / z1) * 360)) / 360 * z1 * pitch, -centre_distance(m, z1, 0, pa)])
+            linear_extrude(eps, center = true)
+                involute_rack_profile(m, z3, 3 * m, pa);
+}
+
+rotate(is_undef($bom) ? 0 : [70, 0, 315])
+    gears();
--- a/tests/png/ball_bearings.png
+++ b/tests/png/ball_bearings.png
--- a/tests/png/cameras.png
+++ b/tests/png/cameras.png
--- a/tests/png/gears.png
+++ b/tests/png/gears.png
--- a/tests/png/pcb.png
+++ b/tests/png/pcb.png
--- a/tests/png/rails.png
+++ b/tests/png/rails.png
--- a/tests/rails.scad
+++ b/tests/rails.scad
@@ -25,10 +25,10 @@ use <../vitamins/nut.scad>
 sheet = 3;

 module rails()
-    layout([for(l = rails) carriage_width(rail_carriage(l))], 25)
+    layout([for(l = rails) carriage_width(rail_carriage(l))], 20)
        rotate(-90) {
            rail = rails[$i];
-            length = rail == MGN15 ? 260 : 200;
+            length = 200;
            screw = rail_screw(rail);
            nut = screw_nut(screw);
            washer = screw_washer(screw);
--- a/utils/gears.scad
+++ b/utils/gears.scad
@@ -0,0 +1,131 @@
+//
+// NopSCADlib Copyright Chris Palmer 2020
+// nop.head@gmail.com
+// hydraraptor.blogspot.com
+//
+// This file is part of NopSCADlib.
+//
+// NopSCADlib is free software: you can redistribute it and/or modify it under the terms of the
+// GNU General Public License as published by the Free Software Foundation, either version 3 of
+// the License, or (at your option) any later version.
+//
+// NopSCADlib is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
+// without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
+// See the GNU General Public License for more details.
+//
+// You should have received a copy of the GNU General Public License along with NopSCADlib.
+// If not, see <https://www.gnu.org/licenses/>.
+//
+
+//
+//! Utilities for making involute gears.
+//!
+//! Formulas from <https://khkgears.net/new/gear_knowledge/gear_technical_reference/involute_gear_profile.html>
+//! and <https://www.tec-science.com/mechanical-power-transmission/involute-gear/calculation-of-involute-gears/>
+//!
+//! ```involute_gear_profile()``` returns a polygon that can have the bore and spokes, etc, subtracted from it before linear extruding it to 3D.
+//! Helical gears can be made using ```twist``` and bevel gears using ```scale``` parameters of ```linear_extrude()```.
+//!
+//! Gears with less than 19 teeth (when pressure angle is 20) are profile shifted to avoid undercutting the tooth root. 7 teeth is considered
+//! the practical minimum.
+//!
+//! The clearance between tip and root defaults to module / 6, but can be overridden by setting the ```clearance``` parameter.
+//!
+//! The origin of the rack is the left end of the pitch line and its width is below the pitch line. I.e. it does not include the addendum.
+//
+include <core/core.scad>
+use <maths.scad>
+
+function involute(r, u) = let(a = degrees(u), c = cos(a), s = sin(a)) r * [c + u * s, s - u * c]; //! Involute of circle radius r at angle u in radians
+
+function profile_shift(z, pa) = z ? max(1 - z * sqr(sin(pa)) / 2, 0) : 0; //! Calculate profile shift for small gears
+
+function centre_distance(m, z1, z2, pa) = //! Calculate distance between centres taking profile shift into account
+    let(x1 = profile_shift(z1, pa), x2 = profile_shift(z2, pa)) m * (z1/2 + z2/2 + x1 + x2);
+
+module involute_gear_profile(m, z, pa = 20, clearance = undef, steps = 20) { //! Calculate gear profile given module, number of teeth and pressure angle
+    assert(z >= 7, "Gears must have at least 7 teeth.");
+    d = m * z;                                                  // Reference pitch circle diameter
+    x = profile_shift(z, pa);                                   // Profile shift
+    c = is_undef(clearance) ? m / 6 : clearance;                // Clearance from tip to root
+
+    base_d = d * cos(pa);                                       // Base diameter
+    root_r = d / 2 + m * (x - 1) - c;                           // Root radius (dedendum circle radius)
+    tip_d = d + 2 * m * (1 + x);                                // Tip diameter (addendum circle diameter)
+    tpa = acos(base_d / tip_d);                                 // Tip pressure angle
+    inva = tan(pa) - radians(pa);                               // Involute alpha
+    invaa = tan(tpa) - radians(tpa);                            // Involute alphaa
+    ta =  PI / (2 * z) + 2 * x * tan(pa) / z + inva - invaa;    // Tooth tip thickness angle, radians
+    crest_w = ta * tip_d;                                       // Crest width
+    umax = sqrt(sqr(tip_d / base_d) - 1);                       // Max value of the involute parameter
+
+    base_r = base_d / 2;
+    p1 = involute(base_r, 0);
+    p2 = involute(base_r, umax);
+    dist = norm(p2 - p1);                                        // distance between beginning and end of the involute curve
+
+    base_angle = 2 * acos((sqr(base_r) + sqr(tip_d / 2) - sqr(dist)) / base_r / tip_d) + degrees(2 * ta);
+    root_angle = 360 / z - base_angle;
+    root_circle_r = base_r * sin(root_angle / 2);
+
+    if(!is_undef($show_numbers) && $show_numbers) {
+        echo(d=d);
+        echo(base_d=base_d);
+        echo(tip_d=tip_d);
+        echo(tpa = tpa);
+        echo(inva=inva);
+        echo(invaa=invaa);
+        echo(x=x);
+        echo(ta=ta);
+        echo(crest_w=crest_w);
+        echo(umax = umax);
+        echo(base_angle=base_angle);
+        echo(root_angle=root_angle);
+    }
+    involute = [for(i = [0 : steps], u = umax * i / steps) involute(base_r, u)]; // involute for the bottom side of the tooth
+    truncated = [for(p = involute) if((rot2_z(-base_angle / 2) * p).y <= 0) p];  // removed any above the centreline to prevent overlap
+    reflection = reverse([for(p = truncated) rot2_z(base_angle) * [p.x, -p.y] ]); // reflect and rotate to make the top edge
+
+    root = reverse([for(a = [90 : 180 / steps : 270]) rot2_z(base_angle + root_angle / 2) * ([base_r, 0] + root_circle_r * [cos(a), sin(a)]) ]);
+    tooth = concat(truncated, reflection, root);
+    gear = concat([for(i = [0 : z - 1], p = tooth) rot2_z(i * 360 / z) * p]);
+    rotate(-base_angle / 2)
+        union() {
+            polygon(gear);
+
+            circle(root_r);
+        }
+}
+
+module involute_rack_profile(m, z, w, pa = 20, clearance = undef) { //! Calculate rack profile given module, number of teeth and pressure angle
+    p = PI * m;                                     // Pitch
+    ha = m;                                         // Addendum
+    hf = 1.25 * m;                                  // Dedendum
+    hw = 2 * m;                                     // Working depth
+    h = ha + hf;                                    // Tooth depth
+    c = is_undef(clearance) ? m / 4 : clearance;    // Tip root clearance
+    crest_w = p / 2 - 2 * ha * tan(pa);             // Crest width
+    base_w = crest_w + 2 * hw * tan(pa);            // Base width
+    root_w = p - base_w;                            // Root width
+    clearance_w = root_w - 2 * c * tan(pa);         // Width of clearance without fillet
+    kx = tan(pa / 2 + 45);                          // Fillet ratio of radius and xoffset
+    pf = min(0.38 * m, kx * clearance_w / 2);       // Dedendum fillet radius
+    x = pf / kx;                                    // Fillet centre x offset from corner
+
+    tooth = [ [root_w / 2, -hw / 2], [p / 2 - crest_w / 2, ha], [p / 2 + crest_w / 2, ha], [p - root_w / 2, -hw / 2] ];
+    teeth = [for(i = [0 : z - 1], pt = tooth) [pt.x + i * p, pt.y] ];
+
+    difference() {
+        polygon(concat([[0, -w], [0, -hf]], teeth, [[z * p, -hf ], [z * p, -w]])); // Add the corners
+
+        for(i = [0 : z])                                // Add fillets
+            hull() {
+                for(side = [-1, 1])
+                    translate([i * p + side * (clearance_w / 2 - x), -hf + pf])
+                        circle(pf);
+
+                translate([i * p, -hw /2 + eps / 2])    // Need to extend to fillet up to meet the root at high pressure angles
+                    square([root_w, eps], center = true);
+           }
+    }
+}
--- a/utils/maths.scad
+++ b/utils/maths.scad
@@ -20,7 +20,10 @@
 //
 //! Maths utilities for manipulating vectors and matrices.
 //
-function sqr(x) = x * x;
+function sqr(x) = x * x;                        //! Square x
+function radians(degrees) = degrees * PI / 180; //! Convert radians to degrees
+function degrees(radians) = radians * 180 / PI; //! Convert degrees to radians
+

 function translate(v) = let(u = is_list(v) ? len(v) == 2 ? [v.x, v.y, 0] //! Generate a 4x4 translation matrix, ```v``` can be ```[x, y]```, ```[x, y, z]``` or ```z```
                                                         : v
@@ -63,6 +66,12 @@ function rot3_z(a) = //! Generate a 3x3 matrix to rotate around z
          [ s,  c,  0],
          [ 0,  0,  1] ];

+function rot2_z(a) = //! Generate a 2x2 matrix to rotate around z
+    let(c = cos(a),
+        s = sin(a))
+        [ [ c, -s],
+          [ s,  c] ];
+
 function scale(v) = let(s = is_list(v) ? v : [v, v, v]) //!  Generate a 4x4 matrix that scales by ```v```, which can be a vector of xyz factors or a scalar to scale all axes equally
                        [
                          [s.x, 0,   0,   0],
--- a/vitamins/ball_bearings.scad
+++ b/vitamins/ball_bearings.scad
@@ -16,11 +16,12 @@
 // You should have received a copy of the GNU General Public License along with NopSCADlib.
 // If not, see <https://www.gnu.org/licenses/>.
 //
-BB624 =  ["624",  4,  13, 5, "blue",      1.2, 1.2];  // 624 ball bearing for idlers
-BB608 =  ["608",  8,  22, 7, "OrangeRed", 1.4, 2.0];  // 608 bearings for wades
-BB6200 = ["6200", 10, 30, 9, "black",     2.3, 3.6];  // 6200 bearings for KP pillow blocks
-BB6201 = ["6201", 12, 32, 10, "black",    2.4, 3.7];  // 6201 bearings for KP pillow blocks
-BB6808 = ["6808", 40, 52, 7, "black",     1.5, 1.6];
-ball_bearings = [BB624, BB608, BB6200, BB6201, BB6808];
+BBSMR95 =  ["SMR95", 5,  9,  2.5, "silver",    0.5, 0.7];  // SMR95 ball bearing for FlexDrive extruder
+BB624   =  ["624",   4,  13, 5,   "blue",      1.2, 1.2];  // 624 ball bearing for idlers
+BB608   =  ["608",   8,  22, 7,   "OrangeRed", 1.4, 2.0];  // 608 bearings for wades
+BB6200   = ["6200",  10, 30, 9,   "black",     2.3, 3.6];  // 6200 bearings for KP pillow blocks
+BB6201   = ["6201",  12, 32, 10,  "black",     2.4, 3.7];  // 6201 bearings for KP pillow blocks
+BB6808   = ["6808",  40, 52, 7,   "black",     1.5, 1.6];
+ball_bearings = [BBSMR95, BB624, BB608, BB6200, BB6201, BB6808];

 use <ball_bearing.scad>
--- a/vitamins/camera.scad
+++ b/vitamins/camera.scad
@@ -23,10 +23,38 @@
 include <../utils/core/core.scad>
 use <pcb.scad>

-function camera_pcb(type)         = type[2]; //! The PCB part of the camera
-function camera_lens_offset(type) = type[3]; //! Offset of the lens center from the PCB centre
-function camera_lens(type)        = type[4]; //! Stack of lens parts, can be round, rectanular or rounded rectangular, with optional tapered aperture
-function camera_connector(type)   = type[5]; //! The flex connector block for the camera itself
+function camera_pcb(type)           = type[2]; //! The PCB part of the camera
+function camera_lens_offset(type)   = type[3]; //! Offset of the lens center from the PCB centre
+function camera_lens(type)          = type[4]; //! Stack of lens parts, can be round, rectanular or rounded rectangular, with optional tapered aperture
+function camera_connector_pos(type) = type[5]; //! The flex connector block for the camera itself's position
+function camera_connector_size(type)= type[6]; //! The flex connector block for the camera itself's size
+
+module camera_lens(type, offset = 0) //! Draw the lens stack, with optional offset for making a clearance hole
+    color(grey(20))
+        translate(camera_lens_offset(type))
+            for(p = camera_lens(type)) {
+                size = p[0];
+                r = p[1] + offset;
+                app = p[2];
+                if(size.x)
+                    rounded_rectangle(size + [2 * offset, 2 * offset, round_to_layer(offset)], r, center = false);
+                else
+                    translate_z(size.y)
+                        rotate_extrude()
+                            difference() {
+                                square([r, size.z + round_to_layer(offset)]);
+
+                                if(app)
+                                    translate([0, size.z])
+                                        hull() {
+                                            translate([0, -eps])
+                                                square([app.y, eps * 2]);
+
+                                            translate([0, -app.z])
+                                                square([app.x, app.z]);
+                                        }
+                            }
+            }

 module camera(type) {           //! Draw specified PCB camera
    vitamin(str("camera(", type[0], "): ", type[1]));
@@ -36,36 +64,14 @@ module camera(type) {           //! Draw specified PCB camera
        pcb(pcb);

    translate_z(pcb_thickness(pcb)) {
-        color(grey(20))
-            translate(camera_lens_offset(type))
-                for(p = camera_lens(type)) {
-                    size = p[0];
-                    r = p[1];
-                    app = p[2];
-                    if(size.x)
-                        rounded_rectangle(size, r, center = false);
-                    else
-                        translate_z(size.y)
-                            rotate_extrude()
-                                difference() {
-                                    square([r, size.z]);
+        camera_lens(type);

-                                    if(app)
-                                        translate([0, size.z])
-                                            hull() {
-                                                translate([0, -eps])
-                                                    square([app.y, eps * 2]);
-
-                                                translate([0, -app.z])
-                                                    square([app.x, app.z]);
-                                            }
-                                }
-                }
-        conn = camera_connector(type);
+        conn = camera_connector_size(type);
        if(conn) {
+            pos = camera_connector_pos(type);
            color(grey(20))
-                translate(conn[0])
-                    rounded_rectangle(conn[1], 0.5, center = false);
+                translate(pos)
+                    rounded_rectangle(conn, 0.5, center = false);

            flex = [5, 0.1];
            color("orange")
@@ -74,8 +80,8 @@ module camera(type) {           //! Draw specified PCB camera
                        translate(camera_lens_offset(type) + [0, camera_lens(type)[0][0].y / 2])
                            cube([flex.x, eps, flex.y], center = true);

-                    translate_z(conn[1].z - flex.y)
-                        translate(conn[0] - [0, conn[1].y / 2])
+                    translate_z(conn.z - flex.y)
+                        translate([camera_lens_offset(type).x, pos.y] - [0, conn.y / 2])
                             cube([flex.x, eps, flex.y], center = true);
                }
        }
--- a/vitamins/cameras.scad
+++ b/vitamins/cameras.scad
@@ -21,8 +21,8 @@ include <smds.scad>
 rpi_camera_v1_pcb = ["", "",  25, 24, 1, 0, 2.1, 0, "green", false, [[2, -2], [-2, -2], [2, 9.6], [-2, 9.6]],
    [
        [12,   3.25,  0, "-flat_flex", true],
-        [-4.5, -4,    0, "smd_led", LED0603, "red"],
-        [-5.5, -3,    0, "smd_res", RES0603, "10K"],
+        [-4.5, -5,    0, "smd_led", LED0603, "red"],
+        [-5.5, -4,    0, "smd_res", RES0603, "1K2"],
    ],
    []];

@@ -32,7 +32,22 @@ rpi_camera_v1 = ["rpi_camera_v1", "Raspberry Pi camera V1", rpi_camera_v1_pcb, [
        [[0, 0, 4], 7.5 / 2],
        [[0, 0, 5], 5.5 / 2, [1.5/2, 2/2, 0.5]],
    ],
-    [[0, 12 - 1.5 - 2.5], [8, 5, 1]]
+    [0, 12 - 1.5 - 2.5], [8, 5, 1]
+];
+
+rpi_camera_v2_pcb = ["", "",  25, 23.862, 1, 2, 2.2, 0, "green", false, [[2, -2], [-2, -2], [2, -14.5], [-2, -14.5]],
+    [
+        [12.5,   2.75,  0, "-flat_flex", true],
+    ],
+    []];
+
+rpi_camera_v2 = ["rpi_camera_v2", "Raspberry Pi camera V2", rpi_camera_v2_pcb, [0, 9.6 - 12],
+    [
+        [[8.5, 8.5, 3], 0],
+        [[0, 0, 4], 7.5 / 2],
+        [[0, 0, 5], 5.5 / 2, [1.5/2, 2/2, 0.5]],
+    ],
+    [-13.8 + 12.5, 23.862 / 2 - 4.7], [8.5, 4, 1]
 ];

 rpi_camera_pcb = ["", "",  36, 36, 1.6, 0, 3.2, 0, "green", false, [[3.5, -3.5], [-3.5, -3.5], [3.5, 3.5], [-3.5, 3.5]],
@@ -50,9 +65,9 @@ rpi_camera = ["rpi_camera", "Raspberry Pi focusable camera", rpi_camera_pcb, [0,
        [[0, 0,  12], 6],
        [[0, 11, 4.3], 14 / 2, [8/2, 11/2, 1]],
    ],
-    [[0, 18 - 1.5 - 2.5], [8, 5, 1]]
+    [0, 18 - 1.5 - 2.5], [8, 5, 1.6]
 ];

-cameras = [rpi_camera_v1, rpi_camera];
+cameras = [rpi_camera_v1, rpi_camera, rpi_camera_v2];

 use <camera.scad>
--- a/vitamins/pcb.scad
+++ b/vitamins/pcb.scad
@@ -53,6 +53,8 @@ function pcb_accessories(type)  = type[12]; //! List of accessories to go on the
 function pcb_grid(type)         = type[13]; //! Grid if a perfboard
 function pcb_polygon(type)      = type[14]; //! Optional outline polygon for odd shaped boards
 function pcb_screw(type, cap = hs_cap) = Len(type[15]) ? type[15] : find_screw(cap, screw_smaller_than(pcb_hole_d(type))); //! Mounting screw type
+function pcb_size(type) = [pcb_length(type), pcb_width(type), pcb_thickness(type)]; //! Length, width and thickness in a vector
+

 function pcb_grid_pos(type, x, y, z = 0) = //! Returns a pcb grid position
    [-pcb_length(type) / 2 + pcb_grid(type).x + 2.54 * x,
@@ -636,14 +638,13 @@ module flex(cutout = false) { //! Draw flexistrip connector

                        translate([0, -w / 2 + slot_offset + slot_w / 2])
                            square([slot_l, slot_w], center = true);
-
                    }
        }
    }
 }

 small_ff = [[11.8, 0.9], [17, 1.4, 1.2], [12, 1.6, 1.2], [16, 1.1, 1.2]];
-large_ff = [[16,  1.25], [22, 1.5, 2.25],[16, 4.0, 2.5], [21, 0,   2.5]];
+large_ff = [[16,  1.25], [22, 1.5, 2.5], [16, 4.0, 2.5], [21, 0,   2.5]];

 function ff_slot(type)  = type[0]; //! Flat flex slot size
 function ff_latch(type) = type[1]; //! Flat flex latch size
@@ -681,8 +682,8 @@ module flat_flex(type, cutout = false) { //! Draw flat flexistrip connector as u
       }

       color(grey(80))
-            translate([-back.x / 2, -w / 2 + back.y])
-                cube([back.x, mid.y, mid.z - eps]);
+            translate([-back.x / 2, -w / 2 + back.y + eps])
+                cube([back.x, mid.y - 2 * eps, mid.z - eps]);
    }
 }

--- a/vitamins/rails.scad
+++ b/vitamins/rails.scad
@@ -25,6 +25,7 @@ MGN5_carriage  = [ 16,   9.6,  12, 6,  1.5, 0,  8 , M2_cap_screw ];
 MGN7_carriage  = [ 23,   14.3, 17, 8,  1.5, 8,  12, M2_cap_screw ];
 MGN9_carriage  = [ 29.7, 20.8, 20, 10, 2,   10, 15, M3_cap_screw ];
 MGN12_carriage = [ 34.7, 21.7, 27, 13, 3,   15, 20, M3_cap_screw ];
+MGN12H_carriage= [ 45.4, 32.4, 27, 13, 3,   20, 20, M3_cap_screw ];
 MGN15_carriage = [ 43.3, 27.7, 32, 16, 4,   20, 25, M3_cap_screw ];
 SSR15_carriage = [ 40.3, 23.3, 34, 24, 4.5, 0,  26, M4_cap_screw ];
 //
@@ -36,9 +37,10 @@ MGN5 = [ "MGN5",  5,  3.6, 5,   15, 3.5, 2.4, 0.8, M2_cs_cap_screw, MGN5_carriag
 MGN7 = [ "MGN7",  7,  5,   5,   15, 4.3, 2.4, 2.6, M2_cap_screw,    MGN7_carriage, M2_cs_cap_screw ];
 MGN9 = [ "MGN9",  9,  6,   7.5, 20, 6.0, 3.5, 3.5, M3_cap_screw,    MGN9_carriage, M3_cs_cap_screw ];
 MGN12= [ "MGN12", 12, 8,   10,  25, 6.0, 3.5, 4.5, M3_cap_screw,   MGN12_carriage, M3_cs_cap_screw ];
+MGN12H=[ "MGN12H",12, 8,    10, 25, 6.0, 3.5, 4.5, M3_cap_screw,   MGN12H_carriage,M3_cs_cap_screw ];
 MGN15= [ "MGN15", 15, 10,  10,  40, 6.0, 3.5, 5.0, M3_cap_screw,   MGN15_carriage, M3_cs_cap_screw ];
 SSR15= [ "SSR15", 15, 12.5,10,  60, 7.5, 4.5, 5.3, M4_cap_screw,   SSR15_carriage, M4_cs_cap_screw ];

-rails = [MGN5, MGN7, MGN9, MGN15, SSR15];
+rails = [MGN5, MGN7, MGN9, MGN12, MGN12H, MGN15, SSR15];

 use <rail.scad>
Author	SHA1	Message	Date
Chris Palmer	7ce055373a	Add rack to mesh with involute spur gears.	2020-07-07 22:36:34 +01:00
Chris Palmer	71ac571346	Added a utility for making involute spur gears	2020-07-06 23:22:11 +01:00
Chris Palmer	e4d93366fa	Added degrees, radians and rot2_z() to maths.scad.	2020-07-06 12:43:24 +01:00
Chris Palmer	f047ac27f7	Added SMR95 ball bearing	2020-07-04 17:30:26 +01:00
Chris Palmer	a9e479d971	Documented camera lens module.	2020-07-04 14:57:01 +01:00
Chris Palmer	47b01af1ea	Added RPI camera V2 Add cameras to lib.scad	2020-07-04 14:54:19 +01:00
Chris Palmer	fe19eba237	Tweaked flat_flex connectors.	2020-07-04 14:14:25 +01:00
Chris Palmer	235f7b86e3	Camera connector position and size separated. Camera_lens() module added.	2020-07-04 09:55:38 +01:00
Chris Palmer	92d7e18b16	Added pcb_size() function.	2020-07-04 09:53:09 +01:00
Chris Palmer	6a7226120f	Fixed RPI camera component positions.	2020-06-30 18:57:14 +01:00
Chris Palmer	8aa00cd041	Added MGN12H rail and included MGN12 in the test.	2020-06-30 09:28:32 +01:00