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With SimMechanics™, you represent a multibody system using blocks. Like all physical modeling products, each block represents a physical component or an abstract entity fundamental to physical modeling, e.g. frames and frame transforms.
By connecting the blocks with connection lines, you define the relationships that unite the physical components into a single system (or subsystem). In a basic model, these physical components include rigid bodies and joints. You can also add forces and torques, motion sensors, and kinematic constraints such as gears.
The figure shows the block diagram of a multibody system—the four-bar linkage. This model contains subsystem blocks to represent the links and pivot mounts. These represent the rigid bodies of the model. The model contains also four Revolute Joint blocks. These represent the joints in the model. Combined, these blocks form the foundation of this model.
While important, rigid body subsystem and joint blocks are not sufficient to represent the four-bar linkage. Other blocks serve important purposes. These include World Frame, Rigid Transform, Mechanism Configuration, and Solver Configuration blocks. The table summarizes their purpose in a multibody model.
|World Frame||Provides the ultimate reference frame in a model. All remaining frames are defined with respect to this frame. It is inertial and it defines absolute rest.|
|Rigid Transform||Applies a fixed spatial relationship between frames. This block defines the offset distance and angle between two frames.|
|Mechanism Configuration||Identifies the gravity vector in a model.|
|Solver Configuration||Provides essential simulation parameters required to simulate the model.|
The figure breaks the four-bar model into its logical components. These are the physical components and abstract entities that you need in order to represent this system.
Each rigid body subsystem contains SimMechanics blocks that represent solids and their spatial relationships˙. The blocks are Solid and Rigid Transform. The figure shows the blocks that model one of the binary links. Three Solid blocks represent the three solid sections of this rigid body—main, peg, and hole sections. Two Rigid Transform blocks represent the fixed spatial relationships between the three solids. You use them to position the peg and hole sections at the ends of the main section.
You can actuate a model by applying a force or torque to a rigid body or to a joint. To represent forces and torques acting on a rigid body, SimMechanics provides a Forces and Torques library. Drag a block from this library and connect it to the rigid body frame(s) that you want to apply the force or torque to.
One block represents an external force or torque—External Force and Torque. The other blocks represent internal forces between two rigid body frames. You can represent a general internal force, using the Internal Force block, or a specific internal force type, using Spring and Damper Force and Inverse Square Law Force blocks. The figure shows how you can use the External Force block to actuate the crank link of the four-bar model.
To represent forces and torques acting at a joint, SimMechanics provides a selection of actuation inputs in each Joint block. Each joint primitive—the basic component of a joint block—provides a selection of actuation inputs that you can select. You can represent a torque acting on a revolute or spherical joint primitive, or a force acting on a prismatic joint primitive. The figure shows how you can use the base-crank revolute joint block to actuate the joint directly.
You can sense motion between two arbitrary rigid body frames. For this task, SimMechanics provides the Transform Sensor block, which you find in the Frames and Transforms library. This block provides the broadest motion sensing capability in SimMechanics. With it, you can sense position, velocity, and acceleration, both rotational and translational, between any two frames in a model. The figure shows how you can use the Transform Sensor block to sense the position coordinates of the coupler link reference frame with respect to the World frame.
To sense motion directly between two rigid body frames connected at a joint, SimMechanics provides a selection of sensing outputs in each joint block. Each joint primitive provides a selection of sensing outputs that you can select. You can sense rotational position, velocity, and acceleration using revolute and spherical joint primitives. You can also sense translational position, velocity, and acceleration using prismatic joint primitives. The figure shows how you can sense the angular position of the coupler-rocker revolute joint directly from the joint block.