08.1 - Project Proposal

Introduction

Our dear friend Daniel suffers from a severe gambling addiction. He is thousands of dollars in debt, and his girlfriend will leave him if he does not stop soon. To break his addiction, we will create a mechanism that can simulate the thrill of horse racing without losing any money! 

Problem Statement

In more technical terms, the goal of our mechanism is to mimic a horse racing event, including a linear motion profile of the horse moving toward the finish line and an oscillating gallop motion profile that mimics a horse’s natural movement. This will occur on two independent horses.

In terms of the force profile, each horse and its respective track will experience variable force and torque inputs throughout the motion to create randomized race outcomes and events. These variations in driving force will determine the relative speeds and outcomes of each horse, introducing unpredictability and simulating the competitive nature of an actual race.

Lastly, in terms of the coordination profile, the galloping motion of the horse must be synchronized with the linear motion of the horse to produce a realistic gait and gallop motion. The oscillating mechanism representing the horse must complete a cyclic motion that is proportional to its linear velocity, which requires coordination between two distinct degrees of freedom. This creates a complex problem that cannot be solved with revolute or prismatic joints that provide only single-axis motion without the ability to synchronize the two movements.

Mechanism

Our device will consist of two identical horse/track mechanisms. The horse will move along its track via a chain and sprocket design that pulls the platform the horse sits atop, driven by an Arduino-controlled electric motor. This part of our design accounts for the linear motion of the horse from the start to the finish point of the track. To create a random effect that enables the race-like behavior of the mechanism, the Arduino will randomly select a winner and vary the supply voltage of the electric motors, thereby changing the speed of the horses, and simulating a race. 

Additionally, to mimic the actual motion of a horse, the galloping/gait of a horse will be displayed through the complex motion of a four-bar, driven by a rack and pinion running parallel to the sprocket-chain setup. Through the coordinated movement of the linear sprocket-chain system combined with the rotation of the gear, the horse will rock back and forth. 

There is also potential to elaborate on the electrical side. For instance, we mentioned the idea of having speakers or lights to celebrate if your horse was correctly chosen. We could also implement a scoreboard system, but that might fall outside the scope of this project. 

Proposed Scope

With the scale of our project being very manageable, we plan on completing the entirety of the proposed project.

With this being said, our project will still require a large amount of analysis to ensure it functions properly. We will need to complete a position analysis for the links to ensure that the horse figure will not collide with any other assembly as our 4-bar moves. Additionally, in order to get the required motion of our 4-bar, we must ensure that the Grashof condition is satisfied. Within our mechanism is a gear-rack system, and in order to get the proper speed, we will need to tweak the size of the gear. Finally, analysis and testing will have to be completed in order to determine the optimal manufacturing method and material for construction.

As for extending the work of our project, we wish to implement a PID control into the motor in order to accurately vary the track speed of each horse versus a linear increase or constant speed. On top of this, we want to add a speaker, as well as lights to signify the victor of the race, and make it as clear as possible.

Preliminary Design

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For our preliminary design, we first need to consider the kinematics of the four-bar “horse” mechanism. For starters, we need to have a Grashof link, as the four-bar uses the full rotation of the gear rotating along the rack as its input link. To achieve this, we must ensure that the sum of our shortest and longest link lengths is smaller than our remaining link lengths to meet the conditions for a full revolution. Additionally, we need to make sure that the motion of the gear determines the position of all links, meaning we need a mobility of 1 DOF. See below for a kinematic diagram of our mechanism and a solved Gruebler/Grashof equation.

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Additionally, a consideration for our design is predicting the path and movement of the output link/joints on the four-bar mechanism itself. This is important, as we want the movement of the links to mimic a horse galloping, meaning a small, smooth arc, driven by the full rotation of the gear. To do this, preliminary position analysis calculations were taken and plotted within MATLAB to understand the potential motion of each point of interest, mainly being the input-coupler pin or point B, and the coupler-output pin or point C. 

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Using these generated graphs, we can see that our preliminary design achieves the desired motion, where point B completes a full 360-degree rotation, and point C travels back and forth along a small arc.