**PDE4905 Engineering Simulation**

**Coursework Assignment 1 – Continuous Simulation**

**Brief**

Create a Simulink Model for the SCARA robot shown in Figures 1 and 2. The motor specifications are appended to this brief.

In your model, you will need to create a subsystem to model the motors taking into account that the moment inertia of robot Arms 1 and 2 combined is not a constant but depends upon the orientation angle of Arm 2.

Figure 1. Side view of the SCARA robot where two motors are used to control the movements of the roboFigure 2. Top view of the SCARA robot showing the relative angle ( ) between Arm 1 and Arm 2.

The inertial load experienced by Motor 1 depends upon the position of the centre of mass of Arm 2 which varies with the angle ( ), shown in Figure 2.

**Data and Specifications**

[COM = Centre of Mass, MI = Moment of Inertia]

**Arm 1 with motor 1**

Mass | m1 | 0.40 kg |

COM | 0.5 m along | |

length | ||

MI about COMS | I1 | 0.001 kg m^{2} |

MI about | J1 | 0.035 kg m^{2} |

Motor 1 axis |

**Arm 2 with motor 2**

Mass | m2 | 0.60 kg |

COM | 0.25 m along | |

length | ||

MI about COMS | I2 | 0.020 kg m^{2} |

MI about | J2 | 0.050 kg m^{2} |

Motor 2 axis |

Both motors are M543E as shown on the datasheet (a separate sheet).

**Variations of the Moment of Inertia**

The moment of inertia of Arm 2 can be considered as a constant about the axis of motor 2; however, the effective moment of inertia of both Arm 1 and Arm 2 (as the whole mechanism) about the axis of motor 1 will depend on the angle ( ) of Arm 2 relative to Arm 1. In general, a cosine rule should be used, but the distance of the COM of Arm 2 to the axis of motor 1 can be approximated by

^{2} = 0.3 + 0.1 cos(θ),

which means that the effective moment of inertia about the base axis can be approximated by the following equation

( ) = 0.37 + 0.12 cos( ) + _{1} [kg m^{2}].

This provides a possibility of approximating the transfer function

1 | = | 1 | ∗ [1 − | 0.12 | cos( )], | ||

( ) + | + | ||||||

0 | 0 |

where J0=0.37+J1=0.405 kg m^{2}.

Implement this approximation in your Simulink model (within your motor subsystem).

**Simulation Tasks**

Based on the above descriptions, you should build a Simulink model to simulate the movements of both Arms 1 and 2 in a single model.

You should carry out some tests on your model with the following scenarios (from rest):

- Rotate motor 1 by 90 degrees, leaving motor 2 stationary.
- Rotate motor 1 by 45 degrees and motor 2 by 45 degrees.
- Rotate motor 1 by 150 degrees and motor 2 by -50 degrees.
- Rotate motor 1 by 60 degrees and motor 2 by -90 degrees.

Illustrate all these movements with simple diagrams and/or Simulink outputs when appropriate.

**Report and Submission**

Write a report describing your model and present results on a series of tests on the model. Your model should be clearly presented, and an evaluation of the model can be discussed in the light of all assumptions made and what limitations they may place on the model. You should also evaluate the robot based on the tests and present recommendations as to the suitability of the design, the choice of motors and other aspects of the robotic arms.

Your report must be in the form of a standard technical report or article to include:

__Abstract__

About 100 words, no more than 150 words.

__Introduction__

Include a brief review of the background and literature, and explanations of continuous modelling, transfer function, etc., citing relevant references when appropriate.

__Methods__

Describe your modelling technique, the structure of your model. Justify your approaches to building the model and cite relevant references when appropriate. If a PID controller is included, describe the background to such an approach and the method of tuning if necessary.

__Results__

Carry out various tests with different scenarios outlined in the Simulation Tasks. Show the results and explain them in detail. Show results and movements in graphs when appropriate.

__Discussion__

Discuss the model and robot performance for all the tests and their implications on the real systems.

Explain the reasons for how motor 1 responds.

__Conclusions__

Draw brief conclusions and evaluate the model and its possible limitations.

*Submit your report and the model file via the *online Moodle system (UniHub).* Make sure that you submit well before the deadline.*

*The report should be submitted as a PDF or Word document (as part 1 when uploading your file). Your model file should be submitted separately (to be uploaded as part 2).*