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< / 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 >
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< li > < a href = "#orge12e7ea" > 1. Solid bodies< / a > < / li >
< li > < a href = "#org6e14a53" > 2. Frames< / a > < / li >
< li > < a href = "#orgbcbe86d" > 3. Joints< / a > < / li >
< li > < a href = "#orgafe97a3" > 4. Measurements< / a > < / li >
< li > < a href = "#orgdee3066" > 5. Excitation< / a > < / li >
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< / 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 >
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< div id = "outline-container-orge12e7ea" class = "outline-2" >
< h2 id = "orge12e7ea" > < span class = "section-number-2" > 1< / span > Solid bodies< / h2 >
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< div class = "outline-text-2" id = "text-1" >
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< 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 >
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< div id = "outline-container-org6e14a53" class = "outline-2" >
< h2 id = "org6e14a53" > < span class = "section-number-2" > 2< / span > Frames< / h2 >
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< div class = "outline-text-2" id = "text-2" >
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< 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 >
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< div id = "outline-container-orgbcbe86d" class = "outline-2" >
< h2 id = "orgbcbe86d" > < span class = "section-number-2" > 3< / span > Joints< / h2 >
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< div class = "outline-text-2" id = "text-3" >
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< 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 >
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< table id = "orgbc35961" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 1:< / span > Degrees of freedom associated with each joint< / caption >
< colgroup >
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< 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 >
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< td class = "org-left" > Telescoping< / td >
< td class = "org-right" > 1< / td >
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< td class = "org-left" > Universal< / td >
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< td class = "org-right" > 2< / td >
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< td class = "org-left" > Weld< / td >
< td class = "org-right" > 0< / td >
< td class = "org-right" > 0< / td >
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< / 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 >
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< table id = "org3352129" border = "2" cellspacing = "0" cellpadding = "6" rules = "groups" frame = "hsides" >
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< caption class = "t-above" > < span class = "table-number" > Table 2:< / span > Joint primitives for each joint type< / caption >
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< 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 >
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< td class = "org-left" > 6-DOF< / td >
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< td class = "org-left" > Bearing< / td >
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< td class = "org-left" > Bushing< / td >
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< td class = "org-left" >   < / td >
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< td class = "org-left" > Cartesian< / td >
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< td class = "org-left" > Constant Velocity< / td >
< td class = "org-left" >   < / td >
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< td class = "org-left" > Cylindrical< / td >
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< td class = "org-left" > Gimbal< / td >
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< td class = "org-left" > x< / td >
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< td class = "org-left" > Rectangular< / td >
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< td class = "org-left" > Revolute< / td >
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< td class = "org-left" > Telescoping< / td >
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< td class = "org-left" > Weld< / td >
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< 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 >
2020-02-25 18:10:20 +01:00
< div id = "outline-container-orgafe97a3" class = "outline-2" >
< h2 id = "orgafe97a3" > < 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 >
2020-02-25 18:10:20 +01:00
< div id = "outline-container-orgdee3066" class = "outline-2" >
< h2 id = "orgdee3066" > < 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 >
2020-03-13 17:40:22 +01:00
< p class = "date" > Created: 2020-03-06 ven. 15:09< / p >
2019-10-16 11:18:06 +02:00
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