103 lines
5.8 KiB
Org Mode
103 lines
5.8 KiB
Org Mode
#+TITLE: Simscape Model
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#+SETUPFILE: ./setup/org-setup-file.org
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* Introduction :ignore:
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A [[https://.mathworks.com/products/simscape.html][simscape]] model permits to model multi-physics systems.
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[[https://mathworks.com/products/simmechanics.html][Simscape Multibody]] permits to model multibody systems using blocks representing bodies, joints, constraints, force elements, and sensors.
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* Solid bodies
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Each solid body is represented by a [[https://mathworks.com/help/physmod/sm/ref/solid.html][solid block]].
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The geometry of the solid body can be imported using a =step= 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 =step= file. They also can be set by hand.
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* Frames
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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.
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They can be defined from the solid body geometry, or using the [[https://mathworks.com/help/physmod/sm/ref/rigidtransform.html][rigid transform block]].
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* Joints
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Solid Bodies are connected with joints (between frames of the two solid bodies).
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There are various types of joints that are all described [[https://mathworks.com/help/physmod/sm/ug/joints.html][here]].
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#+name: tab:joint_dof
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#+caption: Degrees of freedom associated with each joint
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| Joint Block | Translational DOFs | Rotational DOFs |
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|-------------------+--------------------+-----------------|
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| 6-DOF | 3 | 3 |
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| Bearing | 1 | 3 |
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| Bushing | 3 | 3 |
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| Cartesian | 3 | 0 |
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| Constant Velocity | 0 | 2 |
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| Cylindrical | 1 | 1 |
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| Gimbal | 0 | 3 |
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| Leadscrew | 1 (coupled) | 1 (coupled) |
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| Pin Slot | 1 | 1 |
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| Planar | 2 | 1 |
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| Prismatic | 1 | 0 |
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| Rectangular | 2 | 0 |
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| Revolute | 0 | 1 |
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| Spherical | 1 | 3 |
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| Telescoping | 1 | 3 |
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| Universal | 0 | 2 |
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| Weld | 0 | 0 |
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Joint blocks are assortments of joint primitives:
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- *Prismatic*: allows translation along a single standard axis: =Px=, =Py=, =Pz=
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- *Revolute*: allows rotation about a single standard axis: =Rx=, =Ry=, =Rz=
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- *Spherical*: allow rotation about any 3D axis: =S=
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- *Lead Screw*: allows coupled rotation and translation on a standard axis: =LSz=
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- *Constant Velocity*: Allows rotation at constant velocity between intersection through arbitrarily aligned shafts: =CV=
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#+name: tab:joint_primitive
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#+caption: Joint primitives for each joint type
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| Joint Block | Px | Py | Pz | Rx | Ry | Rz | S | CV | LSz |
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|-------------------+----+----+----+----+----+----+---+----+-----|
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| 6-DOF | x | x | x | | | | x | | |
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| Bearing | | | x | x | x | x | | | |
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| Bushing | x | x | x | x | x | x | | | |
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| Cartesian | x | x | x | | | | | | |
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| Constant Velocity | | | | | | | | x | |
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| Cylindrical | | | x | | | x | | | |
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| Gimbal | | | | x | x | x | | | |
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| Leadscrew | | | | | | | | | x |
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| Pin Slot | x | | | | | x | | | |
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| Planar | x | x | | | | x | | | |
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| Prismatic | | | x | | | | | | |
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| Rectangular | x | x | | | | | | | |
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| Revolute | | | | | | x | | | |
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| Spherical | | | | | | | x | | |
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| Telescoping | | | x | | | | x | | |
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| Universal | | | | x | x | | | | |
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| Weld | | | | | | | | | |
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For each of the joint primitive, we can specify the dynamical properties:
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- The *spring stiffness*: either linear or rotational one
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- The *damping coefficient*
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For the actuation, we can either specify the motion or the force:
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- the force applied in the corresponding DOF is provided by the input
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- the motion is provided by the input
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A sensor can be added to measure either the position, velocity or acceleration of the joint DOF.
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Composite Force/Torque sensing:
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- Constraint force
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- Total force: gives the sum across all joint primitives over all sources: actuation inputs, internal springs and dampers.
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* Measurements
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A transform sensor block measures the spatial relationship between two frames: the base =B= and the follower =F=.
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It can give the rotational and translational position, velocity and acceleration.
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The measurement frame should be specified: it corresponds to the frame in which to resolve the selected spatial measurements. The default is =world=.
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If we want to simulate an *inertial sensor*, we just have to choose =B= to be the =world= frame.
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*Force sensors* are included in the joints blocks.
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* Excitation
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We can apply *external forces* to the model by using an [[https://mathworks.com/help/physmod/sm/ref/externalforceandtorque.html][external force and torque block]].
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Internal force, acting reciprocally between base and following origins is implemented using the [[https://mathworks.com/help/physmod/sm/ref/internalforce.html][internal force block]] even though it is usually included in one joint block.
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