Automated Juggler - Rensselaer Polytechnic Institute

Automated Juggler

Team 7John CarpenterShannon Jordan

Dan Grover

Objective

To create a pan and tilt system that will toss a ball into the air, followed by an adjustment of its position, if needed, to catch that same ball on its way down.

Performance SpecificationThe system’s first goal is to throw a ball 1 meter vertically into the air,and catch it on its way down. Using a gear ratio of 3:2, a throwing radius of 0.7908 meters, and a 4 inch diameter “pouch”, the arm will lower 1.2645 radians from a horizontal position, and accelerate at approximately 12.4 rad/s2 at the shaft gear, meaning the motor itself needs to accelerate 8.07 rad/s2. Once the arm is back to its horizontal position, it begins decelerating, causing the ball to launch. It then returns to the horizontal position and waits for the ball to return in order to catch it.

The next goal of the system is to launch the ball forward, approximately twice the length of the arm, and promptly pan around at a maximum speed of 6.0 rad/s in order to catch the ball as it descends on the other side.

Professional and Societal Consideration

The idea of a control system used to launch an object can be applied to many situations, primarily mechanical systems that could resemble a catapult. The systems could vary, including an automatic ball launching machine (pitching machine), for example, ping pong, tennis, or softball, that one could use to practice sports alone, basic military firing equipment, or a satellite launcher that implements gravity assist.

CostsComponents Manufacturer Part Number Cost Quantity Total

Motor Pittman GM8724s016 $112.26 2 $224.52

Large Gear Stock Drive A 6A61-0NF03112 $19.37 2 $38.74

Small Gear Stock Drive A 6A 6-25DF03106 $7.40 2 $14.80

Timing Belt Stock Drive A 6R 6-1150310 $4.12 2 $8.24

Styrofoam Funnel Walmart N/A $1.50 2 $3.00

Miscellaneous Items Walmart N/A $10.00 1 $10.00

Bore Reducer Stock Drive A 7A30-311806 $5.47 1 $5.47

Timing Belt Stock Drive A 6R 6-1090310 $4.21 1 $4.21

Small Gear Stock Drive A 6A 6-8DF03110 $9.91 1 $9.91

Large Gear Stock Drive A 6A 6-2NF03112 $12.33 1 $12.33

Shipping/Handling/Sales Tax

$14.75$3.95$4.18

- $22.88

Total Parts: $315.94

Total Cost of Parts this Semester: $44.92

LaborLabor:

Person Cost/hour Hours Total

Dan $30 200 $6,000

John $30 200 $6,000

Shannon $30 200 $6,000

Total Labor $18,000

Total Cost $18,315.94

ScheduleThe initial proposed schedule was a little too ambiguous, causing us to fall slightly behind at one point in the semester. Once this was recognized, our team caught up with the schedule to accomplish our goal

Task (person) 2/18 2/25 3/3 3/10 3/17 3/24 3/31 4/7 4/14 4/21 4/28

Background Research

Develop Model (John)

Order Parts (All)

Verify Model(All)

Design Control Signal (Dan)

Design Controller (Dan)

Test Controller in Simulink(Shannon)

Test and Refine Controller(All)

Prepare Demo(All)

Write Final Report(All)

Design ProcedureLinear Model: identify parameters such as inertia and friction

Non-linear Model: adding non-linear effects such as Coulomb friction, gravity loading, torque saturation

Model Validation: compare simulation output to actual system output, use to tune models for better fit

Control Design: initially simple proportional control, develop washout filter

Control Tuning: adjust gains to track desired trajectory based on simulation

Performance Verification: implement the controller with actual system, tune as necessary

Design Iteration: modified cradle design, update models

Modifications of Mechanical SystemIn order to increase the possible angular velocity of the system, two new gears were purchased in order to decrease the initial 4:1 gear ratio of the tilt motor. The larger gear has a 0.935 inch diameter, while the smaller one has a 0.609 inch diameter, resulting in a 3:2 gear ratio.

In addition, to increase the velocity at which the ball itself will be launched, a longer rod, 0.7400 meters, as opposed to the previous 0.2794 meters, was implemented in the final design.

A new cradle was also implemented in order to minimize the effect of ball bounce. It was made with a 4 inch diameter wooden hoop, and a slightly elastic fabric pouch.

Quantitative Specifications

Description ValueThrowing arm length 0.7400 mThrowing radius (ball to center of system) 0.7908 mCatching diameter 0.1016 mMass of system 0.6730 kgDesired height of projectile 1.0000 mMaximum speed of Pan motor 6.0 rad/sMaximum speed of Tilt motor 12.8 rad/sRange of motion, Pan motor ≈π radRange of motion, Tilt motor ≈π/2 rad

Pan Friction ID Testing

Pan Motor

Coulomb Friction (Positive) 0.1826 N.m

Coulomb Friction (Negative) -0.1891 N.m

Average Coulomb Friction 0.1859 N.m

Viscous Friction (Positive) 0.0262 N.m.s/rad

Viscous Friction (Negative) 0.0289 N.m.s/rad

Average Viscous Friction 0.0276 N.m.s/rad

Tilt Friction ID Testing

Note:

Non-linear resultsTilt Motor

Coulomb Friction (Positive) 0.1915 N.m

Coulomb Friction (Negative) -0.1840 N.m

Average Coulomb Friction 0.1878 N.m

Viscous Friction (Positive) 0.0202 N.m.s/rad

Viscous Friction (Negative) 0.0206 N.m.s/rad

Average Viscous Friction 0.0204 N.m.s/rad

Tilt Velocity Curves

Trajectory Analysis

At the shaft gear, angular acceleration:

From ,

angular velocity at the shaft gear when the ball is released:

gv

height2

20=

2/4.127908.

81.9 sradrg

th

===••

θ

sradrgh

th

release /6.57908.

)1)(81.9(22===

•

θ

radreleasestart 1.2645

)4.12(26.5

2

22

=== ••

•

θ

θθ

Using standard equations of motion,

Trajectory Analysis

)sin()sgn( θθθθ

τ cCva gB

gratioB

gratioJ

+++=•

•••

τττ 1

max 3.81.241.24max_max_ −−=−=

espeedspeedV

Control Signal

Plug values in equations for a piecewise control signal

19=••

θ rather than 2/4.12 sradrg

th

=

sradrgh

th

release /6.57908.

)1)(81.9(22===

•

θ

radreleasestart 1.2645

)4.12(26.5

2

22

=== ••

•

θ

θθ

Linear Model

sssG

mglsBJssG

dv

0204.0131.01)(

)cos(1)(

2

2

+=

−+=

θ

Non-linear Model

More complex model of Viscous Friction

Previous vs. Current Tilt Friction ID Shape of Curve

Results

Previous: Linear Current: Non-linear

Current has a more dramatic change is velocity for a given step voltage.

Model Verification

Simulated Friction ID on Model

Model Verification

Tested with Various Step Inputs

Controller Design (Linear Continuous)

1064.141.*80)(++

=s

ssC

Closed loop

Controller Design (Linear Discrete)

9845.0391.6406.6*80)(

−−

=z

zzC

System Performance, Unstable

Tracks well but unstable after launch

System Performance, High Gain

Gain too high, causing vibrations

System Performance, Acceptable

Acceptable

Overshoot at launch –does not affect objective of system

Simulink Diagram

Throwing Vertically and Catching

Pan Implementation

Throwing Forward and Panning Around

Recommendations and Enhancements

Use a ball with lower coefficient of restitution

Design a cradle that is stiff, sturdy, and shock absorbing in order to increase consistency of the toss

Mount throwing arm so that it is centered with the pan axis

Attach an electric level (inclinometer) to the tilt axis in order to accurately initialize the system

Add sensors to track ball and correct for error

Juggle multiple balls at once

Extend original arm so that there is a cradle on each side

Have two separate systems, and coordinate their activities

ConclusionThe initial goal of catching a vertical toss was achieved and recorded

The enhanced goal of using the pan motor to quickly spin around and catch the ball was implemented

More difficult than had initially planned, as the arm is not centered about the tilt axis

May have been achieved had time permitted

A few recommendations and enhancements were suggested in order to refine and update the system in the future