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 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 platesA 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 0.24997 and 0.25003 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

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 

motorP

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

Large angle of oscillation with spring

torsionalspring

pivot

center of mass

angle of pendulum

L

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