MECN 4110: Mechanisms Design Mechanisms Design MECN 4110 Professor: Dr. Omar E. Meza Castillo omeza@bayamon.inter.edu http://facultad.bayamon.inter.edu/omeza Department of Mechanical Engineering MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad BIENVENIDOS 2 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 3 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 4 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 Syllabus Problem-Solving Technique: A. B. C. D. E. F. 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. 5 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 6 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 7 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 8 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 Tentative Lectures Schedule Topic Lecture Introduction of Mechanism and Kinematics 9 1, 2 and 3 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 10 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 11 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 12 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 13 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.2 DESIGN PROCESS 14 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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) 15 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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) 16 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.4 UNITS 17 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 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. MSP21 Kinetics: the study of force on system in motion. 18 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.5 THE SCIENCE OF MECHANICS 19 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 20 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.5 THE SCIENCE OF MECHANICS 21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 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, MSP21 or link, which for purposes of kinematics analysis we will assume to be incapable of deformation. 22 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY DOF of rigid body in Space DOF of Rigid body in Plane 23 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.6 DEGREE OF FREEDOM (DOF) OR MOBILITY 24 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.7 TYPES OF MOTION Pure rotation Reference line Reference line 25 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.7 TYPES OF MOTION Pure translation 26 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.7 TYPES OF MOTION Complex Motion : Rotation + Translation q 27 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 28 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.7 LINKS, JONTS AND KINEMATIC CHAINS 29 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 30 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 31 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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: 1. By the type of contact between the elements, line, point or surface. 2. By the number of degrees of freedom allowed at the joint. 3. By the type of physical closure of the joint: either force or form closed. 4. By the number of links joined (order of the joint). 32 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 33 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Lower Pair: Name (symbol) DOF Contains Revolute (R) 1 R Prismatic (P) 1 P Screw or Helical (H) 1 R+P Cylindric (C) 2 R+P Spherical (S) 3 R+R+R Planar or Flat (F) 3 R+P+P MSP21 DOF: Degree of Freedom 34 Planar Mechanism 3-D Mechanism 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Revolute (R): Rotating full pin joint Dq 35 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Prismatic (P): Translating full slider joint DX 36 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Helical (H): 37 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Cylindric (C): 38 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Spherical (S): 39 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: THE SIX LOWER PAIRS Flat (F): 40 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT Roll-slide (Half or RP) joint: Dq DX MSP21 Linkage against Plane (Force close) 41 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.8 JOINT PAIRS: HIGHER PAIRS AND HALF JOINT Higher Pair: 2 DOF DX Dq MSP21 Pin in Slot (Form Close) 42 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 joint Firs t oorder rder ppin in jo int Seco nd orderorder pin jopin int joint Second 43 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 44 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 45 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links in the plane have 6 DOF Dy1 Dq1 Dy2 Dx1 46 Dx2 Dq2 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links connected by a full joint have 4 DOF Dy Dx Dq1 47 Dq2 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 2 links connected by a roll-slide (half) have 5 DOF Dq2 Dx1 Dy Dq1 Dx2 48 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 49 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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 50 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 51 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.10 DETERMINING DEGREE OF FREEDOM OR MOBILITY 52 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 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. 53 MSP21 54 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.12 EXAMPLES 55 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.12 EXAMPLES 56 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad 1.12 EXAMPLES 57 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.12 EXAMPLES 1. Number or links L = 4 2. Number of (full joint) 4 joints J=4 3. Number of ground link G=1 M = 3(4 - 1) – 2x4 M= 1 58 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 1.12 EXAMPLES 1. Number or links L = 9 2. Number of full joints 10 and half joints 2 J=12 3. Number of ground link G=1 M = 3(9 - 1) – 2x12 M= 0 59 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad MSP21 Homework1 http://facultad. bayamon.inter.edu/omeza/ Omar E. Meza Castillo Ph.D. 60 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad ¿Preguntas? Comentarios 61 MSP21 4110: Mechanisms MECN Design- Bayamón Interamericana Universidad GRACIAS 62