This video demonstrate Block Diagram modeling using MapleSim, a toolbox from Maplesoft, using Furuta Pendulum Example.
Transcript:
Hello everyone today we will use MapleSim, a toolbox from Maplesoft, to model Furuta Pendulum.
The schematic diagram of the pendulum is shown on right hand side of the screen. We have horizontal rotating arm, on base of which we have DC motor coupled with gears. At the free end of the horizontal arm we have another hinged link which is free to rotate about horizontal arm. Today we will model only Furuta pendulum the DC motor will be modeled in next presentation. Starting with, we will first place a ground or fixed reference frame. This frame represents the base of the Furuta Pendulum. The next component is revolute joint. Inboard frame of revolute joint is connected to fixed frame. This revolute joint is actuated by a DC motor which we will model in the next presentation. We will assume that the horizontal link is a slender rod with mass concentrated at the center of geometry. The point mass at center of gravity is represented by rigid body. This rigid body is attached to fixed frame by a rigid body frame. The rigid body frame helps to define the translation of rigid body with respect to the frame of adjacent component, in this case fixed frame or ground. The rigid body end of rigid body frame is always connected to rigid body. In this way MapleSim detects the location of rigid body. Similarly, we have another rigid body frame which defines the translation, from rigid body to 2nd revolute joint. This is a good point to save our model and define link parameters.
•We assume the gravity is in global negative z axis direction
•The base revolute joint rotates about local z axis
•Rigid body translation is -L1/2 in local x axis direction with respect to rigid body towards fixed frame and L1/2 in local x-axis direction towards 2nd revolute joint.
•The mass of horizontal link is m1.
•The link is assumed symmetric about local z and y axes. The moment of inertia about z and y axes is I1. The moment of inertia about x axis is assumed to be negligible. All these parameters are defined in the parameters list. The process of parameter defining is trivial and can be easily understood by watching MapleSim webinars. Once we have laid out our horizontal link, we can make a copy of it to model pendulum link.
•Attach revolute joint to outboard frame of rigid body frame of horizontal link. Notice that the axis of rotation for this revolute joint is local x axis.
•Rearrange the components so that it look like Inverted Pendulum.
•Translation of rigid body with respect to local rigid body towards revolute joint is L2/2 in local z axis direction and towards free end is L2/2.
•The mass of pendulum is m2.
•The link is assumed symmetric about local x and y axes. The moment of inertia about x and y axes is I2. The moment of inertia about z axis is assumed to be negligible.
Now our model is ready to simulate.
We can see the pendulum is upright at this point, because we modeled it in upright position. In the perfect world of computer simulation we do not have any disturbance to our pendulum, therefore there is no movement to our pendulum. Let us create one artificial disturbance. Instead of having pendulum perfectly upright in its initial configuration, let us make some initial offset to perfect upright position. This can be done by enforcing initial condition to second revolute joint.
Once again we run the simulation. Now we can see the free fall of the pendulum due to gravity. We can see the effect of inertia coupling between two links. Because of the movements of pendulum the horizontal arm is swinging in this simulation. We can analyze the movement in greater detail by generating required time plot of joint variables. We can attach a probe to the revolute joint to generate plot of the two revolute joint angles. We will attach one probe to outboard rotation frame of base revolute joint and call it motor angle. Similarly connect another probe to 2nd revolute joint and call it Pendulum angle. The probe data can be exported to comma delimited file for further analysis.
In this presentation we have seen MapleSim multibody block-modeling with Furuta Pendulum example. I hope you enjoyed this video. Thank you.
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Automatic Dynamics Equation Generation of Multibody systemsby sumit5333600 views
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