Mechanical Design Calculations

Pioneer P3 DX is the mobile robot base
- Two wheeled base allows turning on the spot
Catapult based bean bag launch mechanism
- Adjust amount of spring tension to change velocity of bean bag
- Adjust stopping location of catapult to change trajectory
Bean bag reloading mechanism
- Simple slot based mechanism to load bean bags
Materials - EPDM Rubber belts, Aluminium Frame, PLA (3D Printed)

The overall mechanical design is a catapult to use a spring constant for a force along with a solenoid to lock the catapult in while obtaining the force.

The rationale for this design is that it would be an easy and compact way to design a way to throw the bean bag. The original design (see Mechanical Calculations)

Mechanical Design Research

Bean bag belt drive

This initial design was chosen to emulate a mechanism to throw tennis balls, but was found to be very complex for this robot design. The formulas used to find this include Vx= Vcos(θ) for the horizontal launch velocity component of V, and Vy = Vsin(θ) for the vertical launch velocity component. Another formula that was used was S = ut+0.5at^2, with S being the distance, a as acceleration and t as time. The approximate distance for this launcher would be 3.82m, and using this the third formula along with the horizontal launch velocity would be 3.82 = Vcos(θ)t+0.5* 0* t^2. For the maximum range, θ was given to be 45 degrees, so that it would then be 3.82 = (v*t) / √2, or t = 5.402 / v.

Next, using the information that the hole on the cornhole table is 0.1638m above ground level and that the Pioneer PD 3X frame has the top plate 0.237m above the ground it is possible to assume that the highest point of the launch mechanism would be 0.30m above that. Hence the bean bag launching point is ~0.537m above ground level. This implies that the corn table hole is at -0.3732m vertically away from the bean bag launch point. Using the third formula again with the vertical component would then be -0.3732 =v*t/√2+ 0.5* -9.81* t^2, and using the t from before solves to get a launching velocity of Vlaunch = 5.842 m/s.

The launch velocity could then be found with Vlaunch = a*t or t = Vlaunch / a, and using the third formula and a distance of 30 cm to accelerate to this velocity could then find the acceleration. This would then be 0.3 = 0*t + 0.5*a*(Vlaunch / a)^2 = 0.5 * (5.842 / a)^2, and then a = 56.881 m/s^2. Using F=ma to find the force (f), and using the mass (m) of a 0.453 kg bean bag, it wold then be F = 0.453 * (58.881 + 9.81 * √2) = 28.09 N, due to considering gravity on the 45 degree launching mechanism. For our design involving a rotating conveyor belt, a practical upper limit on the radius of the pulley on which the belt is wound would be 10cm (to avoid the mechanism sticking out of the robot). Therefore, the total torque provided to the pullies of radius 0.1m is 2.809 N-M.

Lin Engineering Stepper Motors (8718)

The average velocity during the launch process as distance/time = 0.3/ (5.842/56.881) = 2.92m/s. This corresponds to the average motor rps as follows = Vaverage / (2*pi*r) = 2.92/ (2*3.14*0.1) = 4.65 rps. Similarly, at the launch velocity of 5.842m/s, the rps becomes 9.303.

The torque curves for the Lin Engineering stepper motors that were considered for our designs are approximately in between the two torque curves shown above (8718-05R). At 4.65rps (average motor rps during launch), which would get somewhere around 2N-m of force. With 2 motors would get 4N-m of force, which is suitable for this application. Even at the launch velocity rps of 9.303, the combined torque would be 3, which is still greater than the required torque of 2.809 N-M.

However, the cost of suitable stepper motor drivers, 48V lithium ion cells, V belts, stepper motors and the overall complexity involved prompted the group to try a simpler catapult mechanism to be safe for the competition.

Catapult Mechanism Spring Constant Calculations

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