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What kinds of systems are addressed by MechanicalSystems? |
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MechanicalSystems deals with the kinematics and dynamics of
rigid-body systems. It is actually two separate but highly parallel
packages—one for two-dimensional and one for three-dimensional
kinematics. Any number of bodies may be combined by constraints to
form a mechanism of arbitrary complexity. The model may then be solved
numerically to find the position, velocity and acceleration of each
body. If external forces are applied to the
mechanism, MechanicalSystems can find the resulting reaction
forces applied to each body in the model.
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| Q: |
What coordinate systems are used
by MechanicalSystems? |
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By default, MechanicalSystems uses reference-point coordinates. The
position of each two-dimensional body is represented by the coordinates of
its origin and the direction angle of the local axis (x, y,
c). The position of each three-dimensional body is represented
by the coordinates of its origin and four Euler parameters or
quaternion elements (x, y, z, qo, qi,
qj, qk). However, user-defined generalized coordinates
may be assigned to any body and freely mixed with other bodies
represented by a reference point. Using generalized coordinates can
significantly reduce the complexity and increase the performance of a
model.
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| Q: |
What are the symbolic capabilities
of MechanicalSystems? |
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MechanicalSystems generates all constraint equations and equations
of motion symbolically. In general, the resulting mechanism models do not
have closed-form solutions, so they are solved numerically. For those special
cases that have symbolic solutions, Mathematica's built-in symbolic
capabilities may be used to manipulate and solve the constraint equations.
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| Q: |
Can MechanicalSystems solve inverse kinematics
problems? |
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Yes, it can. MechanicalSystems has a very flexible inverse kinematics
(or design synthesis) module. Any number of mathematical conditions may be
specified and applied at any number of different mechanism configurations.
MechanicalSystems will adjust a specified set of design variables,
attempting to find a design that satisfies all of the conditions. The
mathematical conditions may involve positions, velocities, accelerations
or joint reaction forces.
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| Q: |
Does MechanicalSystems do dynamic simulations? |
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MechanicalSystems does both inverse (where the motion is specified
and the reaction forces are sought) and forward (where the applied
forces are specified and the motion profile is sought) dynamic
simulations. MechanicalSystems uses a variable-order, adaptive,
Adams-Bashforth solution method for forward dynamic simulations. For 3D
models using angular coordinates, MechanicalSystems uses a special
integration block that integrates in angular coordinate space and then
does an exact transformation to Euler parameter space. This method
provides highly accurate simulations with large time-steps for models
that would otherwise be limited by the integration of sinusoids
representing their angular orientation.
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| Q: |
Can MechanicalSystems handle simulation problems involving
three-dimensional gyroscopic forces? |
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Yes, it can. Because of the difficulty in tracking the rapidly changing
coordinates of the gyroscopic bodies, gyroscopic problems (where some bodies
in the model are spinning at a much higher frequency than the motion of
interest) suffer in accuracy and efficiency when three-dimensional
reference-point coordinates are used. MechanicalSystems provides
two alternative methods to deal with such problems. First, special
gyroscopic constraints can be used to efficiently represent bodies that spin
about one of their principal axes. Second, and more generally, generalized
angular coordinates may be used to represent the spinning body regardless
of its symmetry or balance.
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| Q: |
Can MechanicalSystems handle problems involving
friction? |
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Yes. The external forces applied to each body in a MechanicalSystems
model are specified as symbolic functions of position, velocity or the
reaction forces at constraints. In this environment, friction at a mechanism
joint is simply an applied force that is a function of the position of the
body and the reaction force at the joint (and possibly the velocity of the
body). MechanicalSystems does not attempt to provide any particular
friction model—the nature of the friction model is up to the user.
Note
that the symbolic expressions given to specify friction forces may have
discontinuities, so it is possible to represent such things as the sign
change in static friction upon a direction reversal.
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| Q: |
What documentation is provided with MechanicalSystems? |
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MechanicalSystems comes with complete documentation that
automatically fully integrates with the searchable Mathematica
help browser. The documentation contains several examples of complete
mechanism models, which may be used as templates for your own
models. A printed manual is also included, except with download versions of the product. Documentation is also available online.
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| Q: |
What do I need to run MechanicalSystems, and how do I
order it? |
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MechanicalSystems 2.2.0 requires Mathematica 10 or greater and
is available for all Mathematica platforms.
MechanicalSystems can be purchased from Wolfram Research or your local
reseller. Pricing and ordering
information is available in our
online store.
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| Q: |
Where can I get help if I have technical questions about
MechanicalSystems? |
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For assistance in installing or operating MechanicalSystems,
contact our Technical Support department or your local reseller.
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