2019-10-16 11:18:06 +02:00
<?xml version="1.0" encoding="utf-8"?>
< !DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
< html xmlns = "http://www.w3.org/1999/xhtml" lang = "en" xml:lang = "en" >
< head >
2021-02-20 23:09:27 +01:00
<!-- 2021 - 02 - 20 sam. 23:08 -->
2019-10-16 11:18:06 +02:00
< meta http-equiv = "Content-Type" content = "text/html;charset=utf-8" / >
< title > Simscape Model< / title >
< meta name = "generator" content = "Org mode" / >
< meta name = "author" content = "Dehaeze Thomas" / >
2021-02-20 23:09:27 +01:00
< link rel = "stylesheet" type = "text/css" href = "https://research.tdehaeze.xyz/css/style.css" / >
< script type = "text/javascript" src = "https://research.tdehaeze.xyz/js/script.js" > < / script >
2019-10-16 11:18:06 +02:00
< / head >
< body >
< div id = "org-div-home-and-up" >
2020-02-25 18:21:17 +01:00
< a accesskey = "h" href = "./index.html" > UP < / a >
2019-10-16 11:18:06 +02:00
|
2021-02-20 23:09:27 +01:00
< a accesskey = "H" href = "../../index.html" > HOME < / a >
2019-10-16 11:18:06 +02:00
< / div > < div id = "content" >
< h1 class = "title" > Simscape Model< / h1 >
< div id = "table-of-contents" >
< h2 > Table of Contents< / h2 >
< div id = "text-table-of-contents" >
< ul >
2021-02-20 23:09:27 +01:00
< li > < a href = "#org0e399eb" > 1. Solid bodies< / a > < / li >
< li > < a href = "#org8fe7328" > 2. Frames< / a > < / li >
< li > < a href = "#orgf4c96ec" > 3. Joints< / a > < / li >
< li > < a href = "#orge58c3e3" > 4. Measurements< / a > < / li >
< li > < a href = "#org6556ccd" > 5. Excitation< / a > < / li >
2019-10-16 11:18:06 +02:00
< / ul >
< / div >
< / div >
< p >
A < a href = "https://.mathworks.com/products/simscape.html" > simscape< / a > model permits to model multi-physics systems.
< / p >
< p >
< a href = "https://mathworks.com/products/simmechanics.html" > Simscape Multibody< / a > permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
< / p >
2021-02-20 23:09:27 +01:00
< div id = "outline-container-org0e399eb" class = "outline-2" >
< h2 id = "org0e399eb" > < span class = "section-number-2" > 1< / span > Solid bodies< / h2 >
2019-12-11 17:09:32 +01:00
< div class = "outline-text-2" id = "text-1" >
2019-10-16 11:18:06 +02:00
< p >
Each solid body is represented by a < a href = "https://mathworks.com/help/physmod/sm/ref/solid.html" > solid block< / a > .
The geometry of the solid body can be imported using a < code > step< / code > file. The properties of the solid body such as its mass, center of mass and moment of inertia can be derived from its density and its geometry as defined by the < code > step< / code > file. They also can be set by hand.
< / p >
< / div >
< / div >
2021-02-20 23:09:27 +01:00
< div id = "outline-container-org8fe7328" class = "outline-2" >
< h2 id = "org8fe7328" > < span class = "section-number-2" > 2< / span > Frames< / h2 >
2019-12-11 17:09:32 +01:00
< div class = "outline-text-2" id = "text-2" >
2019-10-16 11:18:06 +02:00
< p >
Frames are very important in simscape multibody, they defined where the forces are applied, where the joints are located and where the measurements are made.
< / p >
< p >
They can be defined from the solid body geometry, or using the < a href = "https://mathworks.com/help/physmod/sm/ref/rigidtransform.html" > rigid transform block< / a > .
< / p >
< / div >
< / div >
2021-02-20 23:09:27 +01:00
< div id = "outline-container-orgf4c96ec" class = "outline-2" >
< h2 id = "orgf4c96ec" > < span class = "section-number-2" > 3< / span > Joints< / h2 >
2019-12-11 17:09:32 +01:00
< div class = "outline-text-2" id = "text-3" >
2019-10-16 11:18:06 +02:00
< p >
Solid Bodies are connected with joints (between frames of the two solid bodies).
< / p >
< p >
There are various types of joints that are all described < a href = "https://mathworks.com/help/physmod/sm/ug/joints.html" > here< / a > .
< / p >
2021-02-20 23:09:27 +01:00
< table id = "org7462d76" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
2019-10-16 11:18:06 +02:00
< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Degrees of freedom associated with each joint< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-right" / >
< col class = "org-right" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Joint Block< / th >
< th scope = "col" class = "org-right" > Translational DOFs< / th >
< th scope = "col" class = "org-right" > Rotational DOFs< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > 6-DOF< / td >
< td class = "org-right" > 3< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Bearing< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Bushing< / td >
< td class = "org-right" > 3< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Cartesian< / td >
< td class = "org-right" > 3< / td >
< td class = "org-right" > 0< / td >
< / tr >
< tr >
< td class = "org-left" > Constant Velocity< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 2< / td >
< / tr >
< tr >
< td class = "org-left" > Cylindrical< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 1< / td >
< / tr >
< tr >
< td class = "org-left" > Gimbal< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Leadscrew< / td >
< td class = "org-right" > 1 (coupled)< / td >
< td class = "org-right" > 1 (coupled)< / td >
< / tr >
< tr >
< td class = "org-left" > Pin Slot< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 1< / td >
< / tr >
< tr >
< td class = "org-left" > Planar< / td >
< td class = "org-right" > 2< / td >
< td class = "org-right" > 1< / td >
< / tr >
< tr >
< td class = "org-left" > Prismatic< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 0< / td >
< / tr >
< tr >
< td class = "org-left" > Rectangular< / td >
< td class = "org-right" > 2< / td >
< td class = "org-right" > 0< / td >
< / tr >
< tr >
< td class = "org-left" > Revolute< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 1< / td >
< / tr >
< tr >
< td class = "org-left" > Spherical< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Telescoping< / td >
< td class = "org-right" > 1< / td >
< td class = "org-right" > 3< / td >
< / tr >
< tr >
< td class = "org-left" > Universal< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 2< / td >
< / tr >
< tr >
< td class = "org-left" > Weld< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 0< / td >
< / tr >
< / tbody >
< / table >
< p >
Joint blocks are assortments of joint primitives:
< / p >
< ul class = "org-ul" >
< li > < b > Prismatic< / b > : allows translation along a single standard axis: < code > Px< / code > , < code > Py< / code > , < code > Pz< / code > < / li >
< li > < b > Revolute< / b > : allows rotation about a single standard axis: < code > Rx< / code > , < code > Ry< / code > , < code > Rz< / code > < / li >
< li > < b > Spherical< / b > : allow rotation about any 3D axis: < code > S< / code > < / li >
< li > < b > Lead Screw< / b > : allows coupled rotation and translation on a standard axis: < code > LSz< / code > < / li >
< li > < b > Constant Velocity< / b > : Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: < code > CV< / code > < / li >
< / ul >
2021-02-20 23:09:27 +01:00
< table id = "orgac35e84" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
2019-10-16 11:18:06 +02:00
< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Joint primitives for each joint type< / caption >
< colgroup >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< col class = "org-left" / >
< / colgroup >
< thead >
< tr >
< th scope = "col" class = "org-left" > Joint Block< / th >
< th scope = "col" class = "org-left" > Px< / th >
< th scope = "col" class = "org-left" > Py< / th >
< th scope = "col" class = "org-left" > Pz< / th >
< th scope = "col" class = "org-left" > Rx< / th >
< th scope = "col" class = "org-left" > Ry< / th >
< th scope = "col" class = "org-left" > Rz< / th >
< th scope = "col" class = "org-left" > S< / th >
< th scope = "col" class = "org-left" > CV< / th >
< th scope = "col" class = "org-left" > LSz< / th >
< / tr >
< / thead >
< tbody >
< tr >
< td class = "org-left" > 6-DOF< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Bearing< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Bushing< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Cartesian< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Constant Velocity< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Cylindrical< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Gimbal< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Leadscrew< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< / tr >
< tr >
< td class = "org-left" > Pin Slot< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Planar< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Prismatic< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Rectangular< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Revolute< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Spherical< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Telescoping< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Universal< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" > x< / td >
< td class = "org-left" > x< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< tr >
< td class = "org-left" > Weld< / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< td class = "org-left" >   < / td >
< / tr >
< / tbody >
< / table >
< p >
For each of the joint primitive, we can specify the dynamical properties:
< / p >
< ul class = "org-ul" >
< li > The < b > spring stiffness< / b > : either linear or rotational one< / li >
< li > The < b > damping coefficient< / b > < / li >
< / ul >
< p >
For the actuation, we can either specify the motion or the force:
< / p >
< ul class = "org-ul" >
< li > the force applied in the corresponding DOF is provided by the input< / li >
< li > the motion is provided by the input< / li >
< / ul >
< p >
A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
< / p >
< p >
Composite Force/Torque sensing:
< / p >
< ul class = "org-ul" >
< li > Constraint force< / li >
< li > Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.< / li >
< / ul >
< / div >
< / div >
2021-02-20 23:09:27 +01:00
< div id = "outline-container-orge58c3e3" class = "outline-2" >
< h2 id = "orge58c3e3" > < span class = "section-number-2" > 4< / span > Measurements< / h2 >
2019-12-11 17:09:32 +01:00
< div class = "outline-text-2" id = "text-4" >
2019-10-16 11:18:06 +02:00
< p >
A transform sensor block measures the spatial relationship between two frames: the base < code > B< / code > and the follower < code > F< / code > .
< / p >
< p >
It can give the rotational and translational position, velocity and acceleration.
< / p >
< p >
The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is < code > world< / code > .
< / p >
< p >
If we want to simulate an < b > inertial sensor< / b > , we just have to choose < code > B< / code > to be the < code > world< / code > frame.
< / p >
< p >
< b > Force sensors< / b > are included in the joints blocks.
< / p >
< / div >
< / div >
2021-02-20 23:09:27 +01:00
< div id = "outline-container-org6556ccd" class = "outline-2" >
< h2 id = "org6556ccd" > < span class = "section-number-2" > 5< / span > Excitation< / h2 >
2019-12-11 17:09:32 +01:00
< div class = "outline-text-2" id = "text-5" >
2019-10-16 11:18:06 +02:00
< p >
We can apply < b > external forces< / b > to the model by using an < a href = "https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html" > external force and torque block< / a > .
< / p >
< p >
Internal force, acting reciprocally between base and following origins is implemented using the < a href = "https://mathworks.com/help/physmod/sm/ref/internalforce.html" > internal force block< / a > even though it is usually included in one joint block.
< / p >
< / div >
< / div >
< / div >
< div id = "postamble" class = "status" >
< p class = "author" > Author: Dehaeze Thomas< / p >
2021-02-20 23:09:27 +01:00
< p class = "date" > Created: 2021-02-20 sam. 23:08< / p >
2019-10-16 11:18:06 +02:00
< / div >
< / body >
< / html >
