Mechanisms Design MECN 4110 Professor: Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering

BIENVENIDOS

Syllabus Catalog Description: Analysis of mobility and kinematics of mechanisms. Application of the graphical and computerized techniques of position analysis, speed, and acceleration in mechanisms. Design of levies and gears. Introduction to the synthesis of mechanisms. Prerequisites: ENGR 2220 – Computerized Engineering Graphics, MECN 3120 – Vector Mechanics for Engineers: Dynamics. Course Text: Norton, Robert L., Design of Machinery: An Introduction to the Synthesis and Analysis of Mechanisms and Machines, 3rd. Ed., McGraw-Hill, 2004.

Syllabus Absences: On those days when you will be absent, find a friend or an acquaintance to take notes for you or visit the web page. Do not call or send an e-mail the instructor and ask what went on in class, and what the homework assignment is. Homework assignments: Homework problems will be assigned on a regular basis. Problems will be solved using the Problem-Solving Technique on any white paper with no more than one problem written on one sheet of paper. Homework will be collected when due, with your name written legibly on the front of the title page. It is graded on a 0 to 100 points scale. Late homework (any reason) will not be accepted.

Problem-Solving Technique: Syllabus Problem-Solving Technique: Known Find Assumptions Schematic Analysis, and Results Quiz : There are several partial quizzes during the semester. Partial Exams and Final Exam: There are three partial exams during the semester, and a final exam at the end of the semester.

Syllabus Laboratory Reports: There seven or eight experimental laboratories throughout the semester. Laboratory reports must be submitted by each group, one week after the experiment is done. The report must be written in English, in a professional format. Final Project: There is a final project, it will consist in the design of a mechanism with application of course knowledge.

Course Grading The total course grade is comprised of homework assignments, quizzes, partial exams, final exam, and a project as follows: Homework 10% Quiz 15% Laboratory Reports 20% Partial Exams 20% Final Exam 20% Final Project 15% 100% Cheating: You are allowed to cooperate on homework by sharing ideas and methods. Copying will not be tolerated. Submitted work copied from others will be considered academic misconduct and will get no points.

Course Materials Most Course Material (Course Notes, Handouts, Homework, Final Project, and Communications) on Web Page: http://facultad.bayamon.inter.edu/omeza/MECN4110a.htm Power Point Lectures will posted every week or two via Edmodo o the web page. Office Hours: Tuesday and Thursday @ 10:30 to 12:00 AM Email: mezacoe@gmail.com

Tentative Lectures Schedule Topic Lecture Introduction of Mechanism and Kinematics 1, 2 and 3

Reference Myska, David H. Machines & Mechanisms: applied kinematic analysis, 2nd Ed., Prentice Hall, 2002 Sandor, G. N., and Erdman A. G., Mechanism Design: Analysis and Synthesis, 4th. Ed., Prentice Hall, 2001 Waldron, Kenneth J. and Kinzel, Gary L., Kinematics, Dynamics, and Design of Machinery, John Wiley & Sons, Inc, 2004.

Introduction and Basic Concepts One thing you learn in science is that there is no perfect answer, no perfect measure. A. O. Beckman Topic 1: Mechanism and Kinematics Introduction and Basic Concepts

Up on completion of this chapter, the student will be able to Course Objectives Up on completion of this chapter, the student will be able to Explain the need for kinematic analysis of mechanism. Define the basic components that comprise a mechanism. Draw the kinematic diagram from a view of a complex mechanism. Compute the number of degrees of freedom of a mechanism. Identify a four bar mechanism and classify it according to its possible motion. Identify a slider crank mechanism.

1.1 ANALYSIS AND SYSTHESIS Analysis: the techniques that allow the designer to critically examine an already existing or proposed design in order to judge its suitability for task. Synthesis (or Design): the process of prescribing the sizes, shapes, material compositions, and arrangements of parts so that the resulting machine will perform the prescribed task.

1.2 DESIGN PROCESS

1.3 THE ENGINEERING REPORT LAB REPORT GUIDE Title Page of Lab Report (2) Table of Contents (3) Abstract (5) Objectives and Introduction (15) Theory (15) Result and Discussion (35) Conclusions (15) References (10)

The U.S. foot-pound-second (fps) system, 1.4 UNITS There are several systems of units used in engineering. The most common in the United States are: The U.S. foot-pound-second (fps) system, The U.S. inch-pound-second (ips) system, and The System International (SI)

1.4 UNITS

1.5 THE SCIENCE OF MECHANICS Statics: deals with analysis of stationary systems, that is, those in which time is not a factor. Dynamics: deals with systems that change with time. Kinematics: the study of motion, quite apart from the forces which produce that motion. More particularly kinematics is the study of position, displacement rotation, speed, velocity, and acceleration. Kinetics: the study of force on system in motion.

1.5 THE SCIENCE OF MECHANICS

1.5 THE SCIENCE OF MECHANICS Reuleaux’ Definition: Machine: a combination of resistant bodies so arranged that their means the mechanical forces of nature can be compelled to do work accompanied by certain determinate motion. Mechanism: an assemblage of resistant bodies, connected by movable joints, to form a closed kinematic chain with one link fixed and having the purpose of transforming motion. Structure: also a combination of resistant bodies connected by joints, but its purpose is not to d work or to transform motion. A structure is intended to be rigid.

1.5 THE SCIENCE OF MECHANICS

1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY A mechanical system’s mobility (M) can be classified according to the number of degrees of freedom (DOF) that it possesses. The system’s DOF is equal to the number of independent parameters (measurements) that are needed uniquely define its position in space and at any instant of time. This system of the pencil in the plane has three DOF The pencil in the this example represents a rigid body, or link, which for purposes of kinematics analysis we will assume to be incapable of deformation.

1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY DOF of rigid body in Space DOF of Rigid body in Plane

1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY

1.7 TYPES OF MOTION Pure rotation Reference line Reference line

1.7 TYPES OF MOTION Pure translation

Complex Motion : Rotation + Translation 1.7 TYPES OF MOTION Complex Motion : Rotation + Translation

1.7 LINKS, JONTS AND KINEMATIC CHAINS Linkages are the basic building blocks of all mechanisms. A linkage consist of links (or bars), generally considered rigid, which are connected by joints, such as pins (or revolutes), or prismatic joints to form open or closed chains (or loops). Such kinematic chains, with at least one link fixed, become (1) mechanisms if at least two other links retain mobility, or (2) structures if no mobility remains.

1.7 LINKS, JONTS AND KINEMATIC CHAINS

1.7 LINKS, JONTS AND KINEMATIC CHAINS A link is an rigid body that possesses at least two nodes that are points for attachment to other links.

1.7 LINKS, JONTS AND KINEMATIC CHAINS Link of different order: Binary link: one of 2 nodes Ternary link: one of 3 nodes Quaternary link: one of 4 nodes

1.7 LINKS, JONTS AND KINEMATIC CHAINS A joint is an connection between two or more links (at their nodes), which allows some motion, or potential motion, between the connected links. Joints (also called kinematic pairs) can be classified in several ways: By the type of contact between the elements, line, point or surface. By the number of degrees of freedom allowed at the joint. By the type of physical closure of the joint: either force or form closed. By the number of links joined (order of the joint).

1.7 LINKS, JONTS AND KINEMATIC CHAINS The kinematic pairs can be: Lower pair (surface contact): are the joints with surface contact between the pair elements. Higher pair (point or line contact): are the joints with point or line contact between the pair elements.

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Name (symbol) DOF Contains Revolute (R) 1 R Prismatic (P) P Screw or Helical (H) R + P Cylindric (C) 2 R+P Spherical (S) 3 R+R+R Planar or Flat (F) R+P+P Planar Mechanism 3-D Mechanism DOF: Degree of Freedom

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Revolute (R): Rotating full pin joint

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Prismatic (P): Translating full slider joint

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Helical (H):

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Cylindric (C):

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Spherical (S):

1.8 JOINT PAIRS: THE SIX LOWER PAIRS Flat (F):

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT Roll-slide (Half or RP) joint: Linkage against Plane (Force close)

1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT Higher Pair: 2 DOF Pin in Slot (Form Close)

Lower pair or Full joint : 1 DOF joint 1.9 PLANAR MOTION Lower pair or Full joint : 1 DOF joint Higher pair, half joint : > 1 DOF, roll-slider Joint order = number of link joined - 1 First order pin joint Second order pin joint

CRANK: Link that makes a complete revolution and is pivoted to ground. 1.9 PLANAR MOTION KINEMATIC CHAIN: An assemblage of links and joints, interconnected in a way to provide a controlled output motion in response to a supplied input motion. CRANK: Link that makes a complete revolution and is pivoted to ground. ROCKET: Link that has oscillatory (back and forth) rotation and is pivoted to ground. COUPLER (or connecting rod): Link that has complex motion and is not pivoted to ground. GROUND: defined as any link or links that are fixed (nonmoving) with respect to the reference frame.

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY Degree of Freedom (DOF): Number or inputs that need to be provided in order o create a predictable output. Also: number of independent coordinates required to define its position. In Planar Mechanisms: 1 link in the plane has 3 DOF

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links in the plane have 6 DOF

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links connected by a full joint have 4 DOF

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links connected by a roll-slide (half) have 5 DOF

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY Gruebler’s equation DOF or M = 3L – 2J – 3G Where: M=degree of freedom or mobility L= number of links J=number of joints G=number of grounded links (always 1) M = 3(L - 1) – 2J

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY Kutzbatch’s modification of Gruebler’s equation M = 3(L – 1)– 2J1 – J2 Where: M= degree of freedom or mobility L= number of links J1= number of DOF (full) joints J2= number of DOF (half) joints Full Joint = 1 Half Joint = 0.5

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY

1.11 MECHANISMS AND STRUCTURES If the DOF is positive, it will be a mechanism, and the links will have relative motion. If the DOF is exactly zero, then it will be a structure, and no motion is possible. If the DOF is negative, then it is a preloaded structure, which means that no motion is possible and some stresses may also be present at the time of assembly.

Application Problems

1.12 EXAMPLES

1.12 EXAMPLES

1.12 EXAMPLES

Number of (full joint) 4 joints J=4 Number of ground link G=1 1.12 EXAMPLES Number or links L = 4 Number of (full joint) 4 joints J=4 Number of ground link G=1 M = 3(4 - 1) – 2x4 M = 1

Number of full joints 10 and half joints 2 J=12 1.12 EXAMPLES Number or links L = 9 Number of full joints 10 and half joints 2 J=12 Number of ground link G=1 M = 3(9 - 1) – 2x12 M = 0

Homework1  http://facultad. bayamon.inter.edu/omeza/ Omar E. Meza Castillo Ph.D.

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