From 52d5e572bbd32d81976f61cf9d76061b0a88b4a2 Mon Sep 17 00:00:00 2001 From: Wouter Horlings Date: Tue, 7 Jul 2020 16:47:24 +0200 Subject: [PATCH] Add documentation for kinematics model --- implementation/SCARA/01_kinematics/3D.png | Bin 0 -> 35693 bytes .../SCARA/01_kinematics/geometrics.odg | Bin 0 -> 12280 bytes .../SCARA/01_kinematics/geometrics.pdf | Bin 0 -> 8593 bytes .../SCARA/01_kinematics/implementation.md | 32 + .../SCARA/01_kinematics/kinematics.emx | 2333 +++++++++++++++++ .../SCARA/documentation/compatibility.odg | Bin 0 -> 12523 bytes .../SCARA/documentation/compatibility.pdf | Bin 0 -> 12442 bytes .../SCARA/documentation/division.odg | Bin 0 -> 13996 bytes .../SCARA/documentation/division.pdf | Bin 0 -> 12714 bytes .../SCARA/documentation/generaldesign.odg | Bin 0 -> 15383 bytes .../SCARA/documentation/generaldesign.pdf | Bin 0 -> 15781 bytes .../SCARA/documentation/implementation.md | 59 + .../SCARA/spike/inverse_kinematics.emx | 1771 +++++++++++++ .../SCARA/spike/motionprofiletest.emx | 407 +++ .../endeffector/endeffector.3dm | 0 .../endeffector/endeffector.emx | 0 implementation/endeffector/endeffector.scn | 1238 +++++++++ .../endeffector/endeffectorIcon.png | Bin 0 -> 6485 bytes .../{submodel => }/endeffector/gripper.scad | 0 implementation/endeffector/gripperbase.stl | 786 ++++++ implementation/endeffector/markerholder.stl | 1962 ++++++++++++++ .../library/SCARA/inverse_kinematics_v1.emx | 1628 ++++++++++++ .../library/setpoint/rectanglepath.emx | 17 + 23 files changed, 10233 insertions(+) create mode 100644 implementation/SCARA/01_kinematics/3D.png create mode 100644 implementation/SCARA/01_kinematics/geometrics.odg create mode 100644 implementation/SCARA/01_kinematics/geometrics.pdf create mode 100644 implementation/SCARA/01_kinematics/implementation.md create mode 100644 implementation/SCARA/01_kinematics/kinematics.emx create mode 100644 implementation/SCARA/documentation/compatibility.odg create mode 100644 implementation/SCARA/documentation/compatibility.pdf create mode 100644 implementation/SCARA/documentation/division.odg create mode 100644 implementation/SCARA/documentation/division.pdf create mode 100644 implementation/SCARA/documentation/generaldesign.odg create mode 100644 implementation/SCARA/documentation/generaldesign.pdf create mode 100644 implementation/SCARA/documentation/implementation.md create mode 100644 implementation/SCARA/spike/inverse_kinematics.emx create mode 100644 implementation/SCARA/spike/motionprofiletest.emx rename implementation/{submodel => }/endeffector/endeffector.3dm (100%) rename implementation/{submodel => }/endeffector/endeffector.emx (100%) create mode 100644 implementation/endeffector/endeffector.scn create mode 100644 implementation/endeffector/endeffectorIcon.png rename implementation/{submodel => }/endeffector/gripper.scad (100%) create mode 100644 implementation/endeffector/gripperbase.stl create mode 100644 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pythagoras. +Then with the use of a tangent we can find the angle **phi**. +Then filling in the *law of cosines* with **C** calculated and **A** and **B** as arm lengths, we can calculate the angles **a**, **b** and **c**. +As a check we sum these angles and they should add up to the value of Pi. + +Then we add **phi** and **b** to get the corner of the first joint relative to the world frame. +And **c** - Pi + **phi** + **b** gives the angle of the second joint relative to the world frame. + + +## Forward model +The forward model is as follows. +``` +joint1 = A_length*[cos(angle1);sin(angle1)]; +joint2 = B_length*[cos(angle2);sin(angle2)]; +end_effector = joint1 + joint2; +``` +This is then drawn as two arms in a 3D viewer. +![3D view of forward model](3D.png) +It follows the outside of the square. diff --git a/implementation/SCARA/01_kinematics/kinematics.emx b/implementation/SCARA/01_kinematics/kinematics.emx new file mode 100644 index 0000000..084a6e6 --- /dev/null +++ b/implementation/SCARA/01_kinematics/kinematics.emx @@ -0,0 +1,2333 @@ + + + + + + 4.8 +0 + False + C:\users\wouter\My Documents\studie\ma\mahd\implementation\SCARA\01_kinematics\kinematics.emx + 2020-7-10 15:12:13 + +'; + type Mainmodel + end; + implementation bg + submodels + Differentiate 432 256 + description '4.01False + Signal\Block Diagram\Differentiate.emx + 2007-9-26 12:9:46 +'; + type 'Differentiate-Default' + ports + signal in input; + signal out output; + end; + icon bg bottom + figures + group + rectangle 416 240 448 272 color 0 fill 15132390; + text 'd/dt' 432 256 color 16711680 13 bold; + end; + end; + implementation eq +parameters + real initial = 0; // initial value +equations + output = ddt (input, initial); + implementation_end; + Differentiate1 432 112 + description '4.01False + Signal\Block Diagram\Differentiate.emx + 2007-9-26 12:9:46 +'; + type 'Differentiate-Default' + ports + signal in input; + signal out output; + end; + icon bg bottom + figures + group + rectangle 416 96 448 128 color 0 fill 15132390; + text 'd/dt' 432 112 color 16711680 13 bold; + end; + end; + implementation eq +parameters + real initial = 0; // initial value +equations + output = ddt (input, initial); + implementation_end; + inverse_kinematics 312 184 + description ' + + 4.8 + SCARA\inverse_kinematics_v1.emx +1 + False + 2020-7-10 12:26:18 +False + +'; + type 'Submodel-Equation' + ports + signal in input [2,1] {m} ; + signal out angle1 {rad} ; + signal out angle2 {rad} ; + signal out a {rad} ; + signal out b {rad} ; + signal out c {rad} ; + signal out phi {rad} ; + end; + implementation eq +parameters + real global A_length; // length of first arm + real global B_length; // length of second arm + real to_rad = 1 {rad}; +variables + real x {m}, y {m}; + real C_length {m}; // length to x and y. + real angle_sum {rad}; // test angle +equations + x = input[1]; + y = input[2]; + phi = atan2(y, x); + C_length = sqrt(x^2 + y^2); + a = arccos ((B_length^2 + C_length^2 - A_length^2) / (2 * B_length * C_length)); + b = arccos ((A_length^2 + C_length^2 - B_length^2) / (2 * A_length * C_length)); + c = arccos ((A_length^2 + B_length^2 - C_length^2) / (2 * A_length * B_length)); + angle1 = b + phi; + angle2 = angle1 - pi * to_rad + c; + + + + implementation_end; + kinematics 536 184 + description '4.0 + Template\Submodel-Equation.emx +1 + False + 2007-11-1 22:32:1 + False +'; + type 'Submodel-Equation' + ports + signal in angle1; + signal in angle2; + end; + implementation eq +parameters + real global A_length = 0.065; + real global B_length = 0.05; +variables + real joint1[2]{m}; + real joint2[2]{m}; + real end_effector[2]{m}; +equations + joint1 = A_length*[cos(angle1);sin(angle1)]; + joint2 = B_length*[cos(angle2);sin(angle2)]; + end_effector = joint1 + joint2; + implementation_end; + rectanglepath 136 184 + description ' + + 4.8 + setpoint\rectanglepath.emx +1 + False + 2020-7-10 12:30:38 +False + +'; + type 'Submodel-Equation' + ports + signal out output [2,1]; + end; + implementation eq +/* +This will generate coordinates for the box that has to be drawn +*/ +parameters + real w = 0.07{m} ; + real h = 0.05 {m}; + real t = 1 {s}; + real origin[2] = [0.01;0.03] {m}; +variables + real v {m/s}; + real t_w {s}; + real t_h {s}; + real period {s}; + real test1, test2, test3; +initialequations + v = (2*w + 2*h)/t; + t_w = w / v; + t_h = h / v; +equations + period = floor(time / t) * t; + output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1]; + output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2]; +implementation_end; + Splitter1 432 200 + description '4.0 + Signal\Block Diagram\Splitter.emx + 2008-01-17 11:28:29 +1 + False +'; + knot Splitter + ports + signal knot duplicatable out output [1]; + signal knot in input [1]; + end; + icon bg ellipse + figures + ellipse 428.8 196.8 435.2 203.2 color -1 fill 0; + ellipse 427.7 195.7 436.3 204.3 color -1; + terminals + input 432 200 fixed; + end; + implementation eq +equations + collect (output) = input; +implementation_end; + Splitter2 432 176 + description '4.0 + Signal\Block Diagram\Splitter.emx + 2008-01-17 11:28:29 +1 + False +'; + knot Splitter + ports + signal knot duplicatable out output [1]; + signal knot in input [1]; + end; + icon bg ellipse + figures + ellipse 428.8 172.8 435.2 179.2 color -1 fill 0; + ellipse 427.7 171.7 436.3 180.3 color -1; + terminals + input 432 176 fixed; + end; + implementation eq +equations + collect (output) = input; +implementation_end; + end; + connections + inverse_kinematics\angle1 -> Splitter1\input; + inverse_kinematics\angle2 -> Splitter2\input; + rectanglepath\output -> inverse_kinematics\input; + Splitter1\output -> Differentiate\input; + Splitter1\output -> kinematics\angle1; + Splitter2\output -> Differentiate1\input; + Splitter2\output -> kinematics\angle2; + end; + implementation_end; +]]> + + + + + + + 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Therefore we want to keep it as small and light as possible. +In the next image we have a general idea of the design. + +![Rough design idea](generaldesign.pdf) + +## Specifications +The Scara has as goal to move the end-effector in a area of 50 mm high and 70 mm wide. +On of the first tests is to be able to travers that square with in a second. +Therefore it has to achieve an average speed of 240 mm/s. +Al be it not for very long. Probably up to 500 mm/s maximum velocity. + +The marker has to be lifted as well. +That will be the task of the end-effector. + +## Details +The levels of detail that we will implement are at least the following steps. + +### Kinematics +A first model is just a kinematics model without any physics. +If we look at the design it only implements the A and B part of the arms. +And we can just mathematically calculate the position of the arms. +This is usefull to check whether we can even reach all the corners of the square. + +### Simple Physics. +Start adding some Mass to the arms and the marker. +We can learn some basic requirements for the motor that we require. +The current implementation would require some infinite power as we have some instantanious speed. +Thus we have to update our path and induce some control. + +It is probably to make some pathing block where we can put some set points into. + +### Adding motor physics. +Start the better motor physics. +What kind of motor do we need to power the setup. + +### Complex arm structure. +Add the the C, D and E arms. +All the arms should now also have complete inertia and mass specifications. + +### Add parasitics to the arm structure +This has to be reviewed at the point that we get here. + +## Division +The submodels will be divided as follows. +However, during the design I will probably run in more blocks than normal. + +![Division of models](division.pdf) + +The submodels in the division should be compatible with each other. +To avoid that we have to update all our models all the time. +We will build every part of the model in a library for 20-sim. This way it is easy for 20-sim to find the updated models. + +![Compatibility solution between different versions](compatibility.pdf) + + diff --git a/implementation/SCARA/spike/inverse_kinematics.emx b/implementation/SCARA/spike/inverse_kinematics.emx new file mode 100644 index 0000000..30e6a10 --- /dev/null +++ b/implementation/SCARA/spike/inverse_kinematics.emx @@ -0,0 +1,1771 @@ + + + + + + 4.8 +0 + False + C:\users\wouter\My Documents\studie\ma\mahd\implementation\submodel\SCARA\spike\inverse_kinematics.emx + 2020-7-9 16:58:55 + +'; + type Mainmodel + end; + implementation bg + submodels + inverse_kinematics 352 184 + description '4.0 + Template\Submodel-Equation.emx +1 + False + 2007-11-1 22:32:1 + False +'; + type 'Submodel-Equation' + ports + signal in input [2,1] {m} ; + signal out angle1 {rad} ; + signal out angle2 {rad} ; + signal out a {rad} ; + signal out b {rad} ; + signal out c {rad} ; + signal out phi {rad} ; + end; + implementation eq +parameters + real global A_length; // length of first arm + real global B_length; // length of second arm + real to_rad = 1 {rad}; +variables + real x {m}, y {m}; + real C_length {m}; // length to x and y. + real angle_sum {rad}; // test angle +equations + x = input[1]; + y = input[2]; + phi = atan2(y, x); + C_length = sqrt(x^2 + y^2); + a = arccos ((B_length^2 + C_length^2 - A_length^2) / (2 * B_length * C_length)); + b = arccos ((A_length^2 + C_length^2 - B_length^2) / (2 * A_length * C_length)); + c = arccos ((A_length^2 + B_length^2 - C_length^2) / (2 * A_length * B_length)); + angle1 = b + phi; + angle2 = angle1 - pi * to_rad + c; + + + + implementation_end; + rectanglepath 112 184 + description '4.0 + Template\Submodel-Equation.emx +1 + False + 2007-11-1 22:32:1 + False +'; + type 'Submodel-Equation' + ports + signal out output [2,1]; + end; + implementation eq +/* +This will generate coordinates for the box that has to be drawn +*/ +parameters + real w = 0.07{m} ; + real h = 0.05 {m}; + real t = 1 {s}; + real origin[2] = [0.05,0.05]{m}; +variables + real v {m/s}; + real t_w {s}; + real t_h {s}; + real period {s}; + real test1, test2, test3; +initialequations + v = (2*w + 2*h)/t; + t_w = w / v; + t_h = h / v; +equations + period = floor(time / t) * t; + output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1]; + output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2]; +implementation_end; + Submodel2 560 184 + description '4.0 + Template\Submodel-Equation.emx +1 + False + 2007-11-1 22:32:1 + False +'; + type 'Submodel-Equation' + ports + signal in angle1; + signal in angle2; + end; + implementation eq +parameters + real global A; + real global B; +variables + real joint1[2]{m}; + real joint2[2]{m}; + real end_effector[2]{m}; +equations + joint1 = A*[cos(angle1);sin(angle1)]; + joint2 = B*[cos(angle2);sin(angle2)]; + end_effector = joint1 + joint2; + implementation_end; + end; + connections + inverse_kinematics\angle1 -> Submodel2\angle1; + inverse_kinematics\angle2 -> Submodel2\angle2; + rectanglepath\output -> inverse_kinematics\input; + end; + implementation_end; +]]> + + + + + + + Experiment 1 + + + + 4.8 + + + + + + + + + time + Submodel2\end_effector[2] + Submodel2\joint1[2] + Submodel2\end_effector[1] + Submodel2\joint1[1] + rectanglepath\output[1] + rectanglepath\output[2] + rectanglepath\test1 + rectanglepath\test2 + rectanglepath\test3 + Constant\output[1] + Constant\output[2] + + + + GraphPlot + + 1 + false + 16777215 + true + + + true + 15780518 + 12624260 + 0 + 10 + 10 + 10 + false + + 16777215 + true + 1 + model + true + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 10 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + true + true + false + + + -0.049999931062904804 + 0.12000000000000034 + true + 3 + + + + + + 0.019999999999999997 + 0.12 + true + 2 + + + + 0.0 + 5.0 + 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Z:\home\wouter\Documents\studie\ma\mahd\implementation\submodel\SCARA\spike\motionprofiletest.emx + 2020-7-9 14:43:21 + +'; + type Mainmodel + end; + implementation bg + submodels + Submodel1 328 200 + description '4.0 + Template\Submodel-Equation.emx +1 + False + 2007-11-1 22:32:1 + False +'; + type 'Submodel-Equation' + ports + signal out output; + end; + implementation eq +/* Equation Submodel +Enter your equations here. You can use the Toolbar buttons at the top ( Add , f(x) etc. ). +*/ +parameters + string dllname = 'MotionProfiles.dll'; +variables + real x[3]; + real t; +equations + // start typing here + t = time-0.5; + x = dll(dllname,'ProfileCycloidal',t); + output = x[1]; + implementation_end; + end; + connections + end; + implementation_end; +]]> + + + + + + + Experiment 1 + + + + 4.8 + + + + + + + + + time + Submodel1\x[1] + Submodel1\x[2] + Submodel1\x[3] + + + + GraphPlot + + 1 + false + 16777215 + true + + + true + 15780518 + 12624260 + 0 + 10 + 10 + 10 + false + + 16777215 + true + 1 + model + true + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 10 + 34 + 400 + 0 + 0 + 0 + 0 + + + Arial + 12 + 34 + 400 + 0 + 0 + 0 + 0 + + + true + true + false + + + 0.0 + 10.0 + true + 3 + + + + + + -8.0 + 12.0 + true + 2 + + + + 0.0 + 10.0 + true + 2 + + + + 0.0 + 10.0 + true + 2 + + + + + + + + 3355111 + 1 + 3355111 + 0 + true + 1 + 2 + 1 + true + + 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= 0.07{m} ; real h = 0.05 {m}; real t = 1 {s}; real origin[2] = [0.05,0.05]{m}; variables real v {m/s}; real t_w {s}; real t_h {s}; real period {s}; real test1, test2, test3; initialequations v = (2*w + 2*h)/t; t_w = w / v; t_h = h / v; equations period = floor(time / t) * t; output[1] = v*(ramp(period+t_h) - ramp(period + t_w+t_h) - ramp(period + t_w + t_h + t_h)) + origin[1]; output[2] = v*(ramp(period) - ramp(period + t_h) - ramp(period + t_h + t_w) + ramp(period + 2 * t_h + t_w))+ origin[2]; implementation_end; ]]> + + +