ME 2220_SP15_LEC01 - Intro to Kinematics

Prof. Albert Espinoza

Polytechnic University of Puerto Rico

Mechanical Engineering Department

Spring 2015

Professor Info

Albert Espinoza, MSME

Office: L-455

Office Hours: MW (11:00 AM-2:00 PM)

email: aespinoza@pupr.edu

Cell: (281) 798-9737

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Title: Design of Machinery, 5th (2011)

Authors: R.L. Norton

ISBN-13: 9780077421717

Textbook

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This course introduces students to the application of fundamental

concepts of kinematics and kinetics to the analysis and design of

mechanisms in mechanical systems. The course focuses to the design

of linkages, cams, and gears using analytical, graphical, and computer-

aided techniques.

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Course Description

Course Content (Tentative)

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Topic Time (Hrs.)

Introduction. Kinematics Fundamentals 6

Position Analysis 6

Velocity Analysis 6

Acceleration Analysis 6

Dynamic Force Analysis 8

Introduction to Cam Design 4

Introduction to Gears and Gear Trains 6

Tests (2 in-class & final exam) 6

TOTAL 48

1. Partial exams (2) : 60%

2. Project : 20%

3. Final exam (Comprehensive) : 20%

Grading Policy:

A (90-100), B (80-89), C (70-79), D (69-60), and F (0-59)

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Test attendance is mandatory.

No section-switching.

There will be no make-up tests, no show = zero.

Evaluation

After taking this course, the students should be able to:

1. Recognize, illustrate, identify , and calculate the mobility for different types of mechanisms such as the standard four-bar linkage, slider-crank mechanism, five- and six-bar linkage, cam-follower, and gear train systems, among others.

2. Analyze the kinematic and kinetic behavior of mechanisms using CAD software and analytical methods.

3. Develop a translating cam-follower mechanism (given the follower position diagram).

4. Analyze the kinematic behavior of stationary and planetary gear trains (given a gear’s diagram).

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Objectives

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Basic Concepts

Mechanism

System of elements arranged to transmit

motion in a predetermined fashion

Machine:

Collection of components that will do work

Typically designed to provide significant

forces and transmit significant power

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Basic Concepts

Arbitrary distinction, need to consider both in the design of machines

Kinematics

The study of motion without regard to forces

Design desired motions of mechanical components

Kinetics

The study of forces on systems in motion

Provides information for further stress analysis and strength-based design

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Basic Concepts

Key topics for machine design

Analysis

Given a mechanism configuration and input motion, determine their kinematic

output characteristic (trajectories, velocities and accelerations)

Synthesis (Design)

Given output (desired) conditions, find the necessary mechanism configuration

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Degrees of Freedom (aka Mobility)

Number of independent parameters (measurements) which are needed to

uniquely define its position in space at any instant of time

Example: Pencil in a plane

3 DOF (two lengths, one angle)

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

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Types of Motion

All points on the body describe parallel (curvilinear or rectilinear) paths

Pure Translation

A reference line drawn on the body changes its linear position but does not change its angular orientation

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Types of Motion

Body possesses one point (center of rotation) that has no motion with respect

to "stationary" frame of reference.

Pure Rotation

A reference line drawn on the body through the center changes only its angular orientation.

Points on the body (i.e., different from center of rotation) describe arcs about that center.

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Types of Motion

Simultaneous combination of rotation and translation

Complex Motion

Any reference line drawn on the body will change both its linear position and its angular orientation.

Points on the body will travel nonparallel paths, and there will be, at every instant, a center of rotation, which will continuously change location

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Links, Joints and Kinematic Chains

“Rigid” body (at least initially assumed) with at least two nodes (i.e., attachment points)

Link

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

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Links, Joints and Kinematic Chains

Link Types

Crank

Makes complete revolution, pivoted to

ground (2)

Rocker

Oscillatory rotation, pivoted to ground (4)

Coupler

Connecting rod, complex motion (3)

Ground (aka Frame)

Fixed (nonmoving) with respect to reference

frame (could be moving)

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Links, Joints and Kinematic Chains

Connection between two or more links (at their nodes), which allows some motion, or potential motion, between the connected links.

Joint

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

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Links, Joints and Kinematic Chains

Joint – classified by the type of contact (line, point, or surface)

Lower Pair Joints

Contact between joined links occurs at every point of a surface segment

Higher Pair Joints

Contact between joined links occurs at isolated points or along line segments

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012) 20

Links, Joints and Kinematic Chains

Six Possible Lower Pairs (1, 2, 3 DOF)

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Building blocks for more complex joints 21

Links, Joints and Kinematic Chains

Joint – classified by the number of degrees of freedom allowed at the joint

1 DOF (rotation or slide) – Full Joint

Ex: Pin Joint, Slider Joint

2 DOFs (roll + slide) – Half Joint

Ex: roll-slide joint, gears, cams

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012) 22

Links, Joints and Kinematic Chains

Joint – classified by the type of physical closure of the joint.

Form Closed

Force Closed

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

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Links, Joints and Kinematic Chains

Joint – classified by the number of links joined (order of the joint).

Order = # Links-1

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

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Links, Joints and Kinematic Chains

Full/Lower Order Joints

Pins (Revolutes)

Sliders (Prismatic)

Allow 1 DOF 25

Links, Joints and Kinematic Chains

Half/Higher Order Joints

Cams

Gears

Allow 2 DOFs 26

Links, Joints and Kinematic Chains

Kinematic Chain

A mechanism is a chain with at least one grounded link

• Open mechanism – at least one link connected to only one other link

• Closed mechanism – each link connected to two or more links

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Assemblage of links and joints, interconnected to provide controlled output 27

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Kinematic Diagrams

Source: Design of Machinery (4th), R.L. Norton, McGraw-Hill (2012)

Schematic diagrams showing links and joints 29

Kinematic Diagrams

Key Steps

1. Identify the Frame (“ground”), link 1

2. Identify all other links (Label 2, 3, 4, 5, etc.)

3. Identify the joints (Label A, B, C, D, etc.)

4. Identify any other point of interest (load applied, output) (Label X, Y, Z,

etc.)

5. Draw the diagram (using binary, ternary links, prismatic, rotational

joints, etc.)

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Kinematic Diagrams

Example

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Kinematic Diagrams

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Example

Kinematic Diagrams

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Example

Kinematic Diagrams

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Example

Kinematic Diagrams

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Example

Kinematic Diagrams

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Example

Kinematic Diagrams

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Example

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