Design of Motion Systems N. Delson

Analysis in 156A Project  Initial Design  Measurement of Performance  Mathematical Modeling  Optimization  Re-Design

Motion System Components  Bearings  Actuators  Control

Bearings  The role of a bearing is to allow motion in desired DOF while constraining motion in all other DOF.  Good Bearing Systems have: Low friction in the direction of motion Low wobble in constrained DOF.

Constraint Design  Every 6 DOF of an object needs to be explicitly constrained, if it is not a motion direction.  Constraining rotation is usually the hardest and requires 2 contacts points in the plane of rotation.  The designer should explicitly choose the contact points, rather than let the part wobble until it hits “something”

Linear Slide Design Large distance between bearings is critical!

Exact Constraint Design: Robust Bearings at Low Cost  Use the minimum necessary number of constraints  How many bearings support a shaft?  What is the problem with too many constraints?  What is the problem with too few?

Examples of Exact Constraints

Examples of Over Constrained Designs No clearance hole Alignment of more than 2 bearings (if no flexible coupling is present)

Rolling Element Bearings

How Ball Bearings Are Made machine rolls the ball between two very heavy hardened steel plates called rill plates A grade three ball has to be spherical within 3 millionths of an inch and the diameter must be accurate within 30 millionths of an inch. This means that for a grade three quarter-inch ball, the diameter would have to be between and of an inch and the smallest diameter measured on the ball has to be within 3 millionths of the largest diameter.

How Precision Shafts Are Made Centreless grinding is commonly used to produce ground bar stock and chromed bar stock. Ball bearings and other spherical products are also finished using centreless grinding methods.

Design of Robust Structures  Just like bearing design but all 6 DOF are constrained  Rotations cause biggest problems  Use large distance between contact points in each plain of rotation.  Contact points may not be obvious Contact points may not be obvious

Motion System Components  Bearings  Actuators  Control

Actuators  Every actuator has a Torque-Speed curve.  Understanding the physics of the actuators is necessary to understand the advantages and disadvantages of each type.  Static and dynamic analysis is necessary

DC Motors  DC brush motors have a linear torque-speed curve  Stall torque and no-load speed define curve  Power is:  Max power is at mid-point  Curve needs to be adjusted based upon operating voltage

Motion Analysis Categories  Quasi-Static  Constant Velocity  Dynamic analysis including acceleration and deceleration  Closed loop control

Analysis Guidelines  Proper Free Body Diagram (FBD)  List assumptions Indicate if conservative or not-conservative  Use Factor of Safety (F.S) for design choices, but not when comparing measured performance to predictions  Always include discussion section

Quasi-Static Analysis Identifies minimum torque requirements to initiate motion Used a lot in MAE3 but not always approrpaite for MAE156A. Especially not appropriate when?

Constant Velocity Analysis  Easy to implement using Torque-Speed curve  Only valid if acceleration and deceleration duration are significantly shorter than constant velocity duration  How valid is this analysis for the robot contest?

Dynamic Example: Pendulum Motion Pendulum Motion Large angle of oscillation with spring

Dynamic Analysis  Apply F = ma  Define initial conditions  Solution methods: 1. ODE numerically (Euler method, Runga-Katta, other?) in Matlab 2. Use dynamic simulation program, such as Working Model, ProE, or other

Effective Inertia  For even a single DOF system there may be more than a single moving mass: There may be: A translating mass and rotating mass A gear reduction where one mass is moving faster than the other  What is the inertia of the system?

Motion System Components  Bearings  Actuators  Control

Control Considerations  Precision  Over-shoot  Vibration  Stability  Control Theory is large field But if you identify the source of the problem, you are 80% the way to a solution

Mechanical Issues Affecting Control  Gear Backlash  Back drivable vs non-back drivable motors  Driving large inertias  System stiffness