SimMechanics

A Four Bar Mechanism

In this tutorial, you build a model of a planar four bar mechanism and practice using some of the important SimMechanics features:

• Configuring the Mechanical Environment Settings
• Setting Up the Block Diagram
• Configuring the Ground and Joint Blocks
• Configuring the Body Blocks
• Sensing Motion and Running the Model

You are urged to go through Building a Simple Pendulum and Visualizing a Simple Pendulum previously in this chapter before proceeding with this section.

The machine consists of three moving bars of homogeneous steel, two connected at one end each to ground points and a third cross bar connecting the first two. The base acts as an immobile fourth bar, with a Ground at each end. The machine forms a single closed loop, and its motion is confined to two dimensions.

The elementary parts of the machine are the bodies, while the revolute joints are the idealized rotational degrees of freedom (DoFs) at each body-to-body contact point. The bodies and the joints expressing the bodies' relative motions must be translated into corresponding SimMechanics blocks. If you want, you can add elaborations such as Constraints, Drivers, Sensors, and Actuators to this essential block diagram.

Counting the Degrees of Freedom

The three moving bars are constrained to move in a plane. So each bar has two translational and one rotational DoFs, and the total number of machine DoFs, before counting constraints, is 3*(2+1) = 9.

Because the motion of the bars is constrained, however, not all of these nine DoFs are independent:

• In two dimensions, each connection of a body with another body or with a ground point imposes two restrictions (one for each coordinate direction).

• Such a restriction effectively eliminates one of the two body ends as independently moving points, because its motion is determined by the next body's end.

• There are four such body-body or body-ground connections and therefore eight restrictions implicit in the machine's geometry.

The eight restrictions on the nine apparent DoFs reduce the DoFs to one, 9 - 8 = 1. There are four rotational DoFs between bars or between bars and grounds. But three of these are dependent. Specifying the state of one rotational DoF fully specifies the other three.

Figure 2-4: Four Bar Mechanism

Visualizing with Virtual Reality

Configuring the Mechanical Environment Settings