10.3.1 2D Example Mechanism

A model of a two-link planar robot arm is developed to demonstrate the use of SetFree and SolveFree to find the instantaneous free acceleration of a mechanism. The robot arm has a force of unit magnitude, but varying direction, applied to the tip of the second link, while the two revolute joints in the arm are free to rotate. By finding the acceleration vector of the tip that results from a 1-unit applied force at a particular configuration of the arm, the "ellipse of mobility" can be plotted.
Of the four constraints that make up the robot arm model, two are Revolute2 constraints that model the joints between the ground and link 1, and between link 1 and link 2. The other two RelativeAngle1 constraints are present only to set up the initial position of the arm. They are dropped by SetFree to provide two unconstrained degrees of freedom. The parameter loadangle is used to change the direction of the applied load at the tip of link 2.

This loads the Modeler2D package and defines names for each of the body numbers.

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Here are the constraints, bodies, and loads for the robot arm model.

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The model is run with the Solution -> Kinematic option so that initial conditions are available for SolveFree. Here is the reaction torque applied by the locked joint between the ground and link 1.

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Here is the robot arm at its initial configuration.