Digital Prototyping Research Paper
Abstract
This paper is an overview of one important area: Digital Prototyping. It will provide a general description of the process of digital prototyping of a robot arm, what is needed for the process etc. The main topics are: free body diagrams and deriving of the equations and implementing the equations in Matlab using Simulink. After that, results will be discussed.
This paper can be used as a good guide or good advice for creating a digital prototype of robot arm.
Key words: robot, arm, digital, prototype, Simulink, equations etc. Introduction
The robotic arm is a mechanical arm based of the constitution of a human arm. It is a vital part in the industry nowadays replacing some of the tasks in everyday production thus increasing
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the current and the mechanical subsystem i.e. the robotic arm.
The electrical subsystem is the one that is represented by the red line: Figure 5: Electrical Subsystem
This part of the model is based on the following equation i_a=(V_a-K_b θ ̇_m )/R_a where V_a is represented by the Step block with a value of 12 V. After the voltage is constructed, the denominator of the equation is added using a gain with a value of 1/R_a. Finally the emf coefficient Kb is multiplied with the angular velocity of the motor which is represented as the first derivative of the angular displacement of the motor θ_m and it is subtracted from the input voltage using the Add block. The result of this equation is the current i_a which is placed as an input to the mechanical subsystem.
For the second subsystem we need the current as an input and the equation. The final result will be the angular displacements of the motor and from the arm shafts within the arm joint. The second subsystem i.e. the mechanical one is represented in the following portion of the Simulink program:
Figure 6: The mechanical Subsystem
The main equation used in this system is the
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The only thing left is to subtract the product of the angular velocity of the motor shaft and the equivalent moment of damping from the previous product and the result is the angular acceleration of the motor shaft. Using Integrator 1 block we transform the angular velocity of the motor shaft into an angular displacement of the motor shaft. By the rule of proportionality the angular displacement of the arm shaft can be found by multiplying the displacement by the ratio of the number of teeth of the gears of the arm and the motor. The result is the following
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