World and Reference Frames

Two preset frames are available in SimMechanics™: World and Reference. These are standalone frames with respect to which you can define other frames in a model. New frames can in turn serve as the basis to define yet other frames. However, directly or indirectly, all frames depend on either World or Reference frames. Both frames are available as blocks in the Frames and Transforms library.

World Frame

The World frame represents the external environment of a mechanical system. It is always at absolute rest, and therefore experiences zero acceleration. As a consequence, centripetal and other pseudo-forces are not present in the world frame, and it is said to be inertial. Rigidly connecting any frame to the World frame makes that frame also inertial. To add the World frame to a model, use the World Frame block.

The World frame is the ultimate reference frame. Its position and orientation are predefined and do not depend on any other frame. This property makes the World frame invaluable. You can always apply a transform to the World frame and obtain a new frame. Applying a transform to the resulting frame in turn yields more new frames, all indirectly related to the World frame. The result is a frame tree with the World frame at the root. The figure shows such a frame tree for a double-pendulum system.

The double-pendulum block diagram is based on this frame tree. The World Frame block identifies the root of the frame tree. A Revolute Joint block applies the variable transform that relates the World frame to the binary link peg frame. A second Revolute Joint block applies a similar variable transform between the hole and peg frames of adjoining binary links. The figure shows this block diagram.

The World frame is present in every model. However, the World Frame block is strictly optional. If you do not add this block to a model, SimMechanics assigns one of the existing frames as the World frame. This implicit World frame connects to the rest of the model via an implicit 6-DOF joint, which in the absence of counteracting forces allows a machine to fall under gravity.

You can connect multiple World Frame blocks to a model. However, all World Frame blocks represent the same frame. In this sense, the World frame is unique. You can add multiple World Frame blocks to simplify modeling tasks, e.g., sensing motion with respect to the World frame. The figure shows the model of a double-pendulum with two World Frame blocks. Both World Frame blocks represent the same frame.

Reference Frame

The Reference frame represents the root of a rigid body or multibody subsystem. Within a subsystem, it denotes the frame against which all remaining frames are defined. To add a Reference frame, use the Reference Frame block. Use this block to mark the top level of a subsystem frame tree.

Applying a transform to the Reference frame yields other frames. Applying transforms to these other frames yields still more frames. The overall set of frames forms a frame tree with the Reference frame at the root. The figure shows such a frame tree for one of the binary links used in the double-pendulum system.

The block diagram of the binary link subsystem is based on this frame tree. The following figure shows the binary link block diagram. The Reference Frame block identifies the root of the frame tree. Rigid Transform block to_hole adds the hole frame. Rigid Transform block to_peg adds the peg frame. It is a simple task to add the main, peg, and hole solids once these frames are defined.

The distinguishing feature of the Reference frame is that it can move with respect to other frames. Depending on the dynamics of a model, a Reference frame can accelerate, giving rise to pseudo-forces that render this frame non-inertial. Rigidly connecting any frame to a non-inertial Reference frame makes that frame also non-inertial.

The Reference frame is present in every subsystem. However, the Reference Frame block is strictly optional. If you do not add this block to a subsystem, SimMechanics assigns one of the existing frames as the Reference frame.

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