Learn more about SimMechanics

Gimbal - Represent composite joint with three rotational DoFs

Library

Joints/Assembled Joints

Description

The Gimbal block represents a composite joint with three rotational degrees of freedom (DoFs) as three revolute primitives. There are no constraints among the primitives.

Warning A joint with three revolute primitives becomes singular if two or three of the rotation axes become parallel ("gimbal lock"). The simulation stops with an error in this case.

A joint with three revolute primitives must be configured in the initial state with the three revolute primitive axes mutually orthogonal. There are no restrictions on the primitive axes once the simulation starts, except to prevent any two of the primitive axes from becoming parallel.

Satisfying Joint Requirements

A Joint block represents the relative degrees of freedom between two bodies, not the bodies themselves.

You must connect any Joint block to two and only two Body blocks, the base and the follower. All Joints have two connector ports for these connections, defining the direction of joint motion (base to follower). You connect each side of the Joint block to these Body blocks at a Body coordinate system (CS) port.

You specify the joint primitive axes, if any, in the Joint dialog.

Assembly Restrictions on Assembled Joints

This Joint block is assembled and places restrictions on the connected Body CSs.

If the Joint has no prismatic primitives, the origins of the connected Body CSs on either side of the Joint must be spatially collocated points, to within assembly tolerances.
If the Joint has one or more prismatic primitives, the origins of the connected Body CSs must lie in the span of the prismatic axes:
Number of Prismatic Primitives Span of Primitive Axes

One Along the primitive axis

Two In the plane of the primitive axes

Three Anywhere in three-dimensional space

Number of Prismatic Primitives	Span of Primitive Axes
One	Along the primitive axis
Two	In the plane of the primitive axes
Three	Anywhere in three-dimensional space

Dialog Box and Parameters

The dialog has two active areas, Connection parameters and Parameters.

Connection Parameters

The base (B)-follower (F) Body sequence determines the sense of positive motion. Positive rotation is the follower moving around the rotational axis following the right-hand rule.

Current base

When you connect the base (B) connector port on the Gimbal block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Gimbal Base and Follower Body Connector Ports.

The base Body is automatically connected to the first joint primitive R1 in the primitive list in Parameters.

Current follower

When you connect the follower (F) connector port on the Gimbal block to a Body CS Port on a Body, this parameter is automatically reset to the name of this Body CS. See the following figure, Gimbal Base and Follower Body Connector Ports.

The follower Body is automatically connected to the last joint primitive R3 in the primitive list in Parameters.

Number of sensor/actuator ports

Using this spinner menu, you can set the number of extra connector ports needed for connecting Joint Actuator and Joint Sensor blocks to this Joint. The default is 0.

The motion of revolute primitives is specified in angular units.

Gimbal Base and Follower Body Connector Ports

Parameters

Switch between the Axes and Advanced tabs.

Axes Tab

The entries on the Axes tab are required. Each DoF primitive in Gimbal has an entry line. These lines specify the direction of the axes of action of the DoFs that the Gimbal represents.

Name - Primitive

The primitive list states the names and types of joint primitives that make up the Gimbal block: revolute primitives R1, R2, R3.

Axis of Action [x y z]

Enter here as a three-component vector the directional axes defining the allowed motions of these primitives and their corresponding DoFs:

Revolute: axis of rotation

The default vectors are shown in the dialog above. The axis is a directed vector whose overall sign matters.

To prevent singularities and simulation errors, no two of the revolute axes can be parallel.

Reference CS

Using the pull-down menu, choose the coordinate system (World, the base Body CS, or the follower Body CS) whose coordinate axes the vector axis of action is oriented with respect to. This CS also determines the absolute meaning of forces/torques and motion along/about the joint axis. The default is World.

Restricted Parameters