Advanced Dynamics has a limited distribution. So, theideas expounded below may seem innovative and new, yet they are not. The purpose of thispaper is to demonstrate the use of rotation operators to solve this problem and to inspire readersto create other innovative solutions. This is the educational purpose of this paper. Since thissolution is based on rotation operators, and rotation operators are often overlooked in dynamics,let us begin with a brief historical overview of rotation operator. Then, I will start from thedefinition of rotation operator, provide examples of operations, and then verify the solutions. Rotation operator was first introduced by J. W. Gibbs in 1901 as mentioned in Ying’sAdvanced Dynamics [1]. A search of the
activities undertaken by the student.Unfortunately, in recent years, extensive use of solution manuals and replication of answers fromthe solution manual without any understanding has been a major hurdle in the learning process ofthe students. Blind faith in the solution manual rather their own abilities to solve problemsnegatively impacts a student’s conceptual understanding of the principles of Dynamics andtherefore impedes their critical thinking ability. This is a nationwide phenomenon [1], [2], [3]and some important reasons has been traced to – (a) students who are employed outside schoolfind less time in their studies, (b) lack of mathematical and analytical skills discourages studentsfrom trying on their own, and (c) instant gratification of
graphical representation of the right-hand side of Newton’s secondlaw of motion. It is often used together with a free-body diagram (FBD) to represent therelationship between the external forces on a body and the body’s inertial response [1-4] (seeFigure 1). Figure 1FBD and KD [1]As elaborated in [5], from the perspective of solving kinetics problems, it is not necessary to use aKD. However, we need to examine pedagogical benefits from students’ learning perspective. Justlike we cannot underestimate the role of a user manual for beginning users because of itsredundancy for experienced users, we need to revisit the role of the kinetic diagram in the teachingof introductory dynamics. In this paper, I will
body (i.e., a set of rigid elements which are rigidly joined together).Two illustrative examples are considered in this article to both introduce and apply the methodadvocated. These examples will reveal the advantage of moment evaluation about a point that isdifferent from the mass center of the body. When the method is properly applied, the associatedeffort is typically less involved than is experienced in the traditional practices because locatingthe position and assessing the motion of the mass center is often challenging in many problems.Some alternative forms of the moments-of-forces/couples equation for the rotational dynamics ofa rigid body, which is frequently called Euler’s equation in the literature, may be found in [1–3].The author
present day. Here position analysis is taken to mean 1)finding the two remaining unknown angles on the linkage with an input angle given and 2)finding the path of a point on the linkage once all angles are known. The efficiency of positionanalysis has taken on increasing importance in recent years with the widespread use of pathoptimization software for robotic and mechanism design applications.Kinematicians have developed a variety of methods for conducting position analysis, but thesolutions presented in the literature fall into two general families: 1. The angle between the coupler and the rocker is found using the law of cosines. Once this is known, the coupler and rocker angles are found using some combination of the laws of
materialThe proof of concept is being explored using Area Moments of Inertia and Products of Inertia.This paper presents the initial feedback from students and instructor and plans for the future.Introduction:The idea that hands-on models can improve learning is not new: Felder and Silverman famouslyincluded hands-on models as an example of an active teaching.[1] The notion that 3D printingcan make such opportunities more available is not new either.[2] As makerspaces become regularon-campus tools for students, educators have been trying to figure out how to bring thatcapability into the classroom.[3,4]I work principally with Statics in the Mechanical and Aerospace Engineering Department at NCState University where my goal has been to increase the
of their effectiveness, haveproliferated STEM [1]–[9] and business disciplines [10]–[13]. Penner et al. provide a summaryof the findings of 7 studies and the “overall assessment” of the corresponding studies, since 2001[3]. They show that there are mixed results from their survey of studies. However, there isgenerally support for using online homework in classes along with traditional (hand written)homework. Only a few studies have investigated if the mixture of online and hand written homeworkaffects student performance on graded events [14]–[16]. One study found improvement inoverall grades of a Chemistry course, but suggest that scores may have been improved further ifstudents had practiced writing organic compounds by hand [14
. Although graphs and stopmotion photography can be used to infer continuous motion, it can still be difficult to getstudents to appreciate the changing velocities and accelerations involved in the motion ofparticles and rigid bodies. To help overcome this, we have incorporated the use of an advancedmotion analysis system into several of our courses at Cal Poly.The use of motion analysis is nothing new – in fact the physics community has been using suchtechnology for years [1-3]. Some investigators have worked to develop their own motionanalysis software [4] to get around the high costs of most motion capture systems, and othershave recognized the advanced image processing capabilities of MatLab to perform motiontracking [5] (http
EngineeringAbstractEngineering students are often given quantitative problems as homework. Problem solvingprovides students opportunities to retrieve knowledge, apply and adjust conceptualunderstanding, and build analytical skills. Because increased motivation has been shown toproduce better learning outcomes [1] - [3], it makes sense to tailor problems to motivate students.Intuitively, adding contextual elements, such as background information, narrative, images, andlocal references, to problems may be one way of motivating students, but investigation in thisarea has been limited [8] - [10]. Therefore, this study surveyed students to gauge theirperceptions of fundamentally identical problems presented either with or without significantcontextual elements. The primary
and challenge exclusionary thoughts andpractices” (p. 46). In their study on the effects of problem-oriented educational strategies onincreasing the student diversity among community college students, Noravian and Irvine (2014)found that moving from well-structured to ill-structured problem solving is beneficial to studentsand suggested the restructure of engineering education “so that students experience early in theirtraining what engineers do” (p. 294). As stated by King (2011), the low number of people ofcolor and women in engineering can be attributed to the highly quantitative focus and “the lackof evidence of social impact of engineering in the early engineering curriculum” (p. 1).In another effort, Knight et al. (2012) argued for the
) andmultiple degree-of-freedom (MDOF) systems subjected to non-zero initial displacements orvelocities (free response) and/or non-zero forces (forced response). As shown in Figure 1, eachof these categories contains subcategories that relate to a different physical response. In a typicalVibrations course, the topics shown in Figure 1 are usually supplemented by a discussion onvibration control (which is an application of the SDOF and MDOF forced response), continuoussystems and basic finite element analysis (through which continuous systems are approximatedas MDOF systems).The breadth of topics that are covered in a typical Vibrations course and the complexitiesassociated with the mathematical solution of each subcategory can often be frustrating
1 of 14 modes, such as visual and kinesthetic, the major one of which is the convenience of learninganywhere (on the go) without requiring the cognitive load associated with image processing.Learners can benefit from audio material while still performing physical tasks at the same time,such as commute or exercise. Audio learning materials can also be made more easily available andincorporated into students' daily activities if they are accessible on a mobile phone through asoftware application (app). This also allows repetition and practice on the go.A project has been initiated in order to leverage these features and provide students with a highlyaccessible and portable audio app for
effective and fun classroom demonstrations(modules) to aid students in developing their conceptual understanding of moments, afundamental topic in Statics. The motivation for this effort stemmed from anecdotal evidence inthe form of student feedback and observations made during exam grading by the authors. Theevidence suggested that students deemed moments to be one of the most challenging topics inStatics. Since the concept of moment is a recurring theme found throughout the hierarchy ofmechanics courses, the authors created an active demonstration for each Statics subtopicinvolving moments. They include: 1. "At arm's length" – identify the principles of moments and moment arms using a volunteer's shoulder as a pivot point 2
videosand reflect on how they may have impacted their learning.BackgroundThe concept of supplementing student learning with course content based videos has beenpreviously explored by many [1] - [3]. Through various means the benefits they can pose, alongwith alternative methods that can be utilized to assess such benefits, have been determined[3] - [8].With students already being exposed to material through lectures, it is important to consider theways in which the videos are able to add value to the course outside of simply providing content.[1] supports the comparable nature of using video resources to in-class instruction. They explainthat using videos to model a problem and a procedure are “effective for acquiring new skills andmay enhance the
guidelines have been followed for the past 12 years. Details of the assessment may befound in references [1 – 3]. An important difference of ESCC from traditional curriculaelsewhere is our program is student-centered. All difficulties in concepts have been researchedand presented below from a student’s learning point of view.Modern computational focus requires mastery of analytical thoughts to properly understand andimprove computational models. There are some mathematical bottlenecks in achieving this featwhich are discussed separately in another paper [4]. The approach requires reinforcingmathematical understanding in parallel with engineering applications. Many examples andattractive demonstrations are necessary before and during active learning
insubsequent courses.The pressing need to reform the teaching and learning Statics has been established in the pastdecades. To enhance teaching and student learning in Statics, researchers at various institutionshave explored various methods for teaching Statics, such as developing concept map andquantifying students’ conceptual understanding [1, 2, 3], developing on-line homework orlearning modules [4, 5], peer-led-team-learning [6, 7], project-based learning [8], emporium-based course delivery [9], etc. Among them, the flipped-classroom method [10, 11, 12] hasbecome popular in the recent years. In a flipped classroom, the class time is devoted to guidedinstruction where students work through problems with the instructor present to provideassistance
are often considered the most foundational for engineering students.Yet, these courses have become impenetrable from changes in content and pedagogy and areoften abstracted from any human or societal context. One reason for this abstraction may be dueto the understandably prolific use of the “engineering problem-solving method” (EPS) or“engineering as problem definition and solution” (PDS), which teaches students how tomethodically approach a technical problem and produce easily checked solutions [1]. However,the EPS method has perpetuated the dominance of mathematical problem solving as the highestvalue in engineering [2], often unintentionally reinforcing the worldview that technical rigor ismore important than the context in which
exam provides evidence of the assessment’s validity as ameasurement instrument for representational competence. We found a positive correlationbetween students’ accurate and effective use of representations and their score on the multiplechoice test. We gathered additional validity evidence by reviewing student responses on anexam wrapper reflection. We used item difficulty and item discrimination scores (point-biserialcorrelation) to eliminate two questions and revised the remaining questions to improve clarityand discriminatory power. We administered the revised version in two contexts: (1) again as partof the first exam in the winter 2019 Statics course at WCC, and (2) as an extra credit opportunityfor statics students at Utah State
study design paired twosequential rigid-body motion topics in Engineering Mechanics: Dynamics to test the effect offlipped vs. traditional lecture on both student learning and engagement. We alternated instructionalmethodology (traditional lecture + flipping) between the two sections of Dynamics in spring 2018.The traditional lecture sessions were taught with hand-written note lectures (with limited activelearning) and completed two typical numerical homework problems per topic. For the flippedsessions, students watched instructional lecture videos prior to class, worked through a hands-onin-class activity, and completed analytical questions related to the in-class activity whichsubstituted for 1 of the 2 homework problems on each topic. Paired
(FGCU). Success in this course is critical to success in follow-up mechanics coursesand upper-level engineering courses. Data has been collected on students’ performance onhomework, quizzes and exams, and also on the students’ thoughts on learning and coursedelivery. Thus far, we have concluded that the use of traditional hand-written homework,frequent assessment via quizzes [1], or the Pearson Mastering Engineering [2] software forformative assessment did not have a significant impact on students’ performance on exams. Itwas also observed that neither traditional nor online homework scores correlated well with examscores; however, in-class quizzes did correlate with final exam scores. Most recently, using theMastering Engineering Online system
Number:1565066. c American Society for Engineering Education, 2019 Experiments in Community Building within Classrooms of Commuter Students. Part I: The Case of StaticsIntroductionA commuter student has been defined as “a college student who does not live in an on-campusinstitutionally-owned/approved housing, such as a residence hall or a fraternity or sorority house[1]. Using this definition, it has been estimated that approximately 85% of today’s students in theUSA commute to campus [2].The lives of commuter students have three separate parts: life at home, life at work, and life atschool. Juggling the responsibilities from those three aspects of their lives is challenging [3]. Inmany
that students need to have to succeed in senior capstone projects orin professional practice. APM is used to respond to students’ struggles with PBL’s projectmanagement. APM is an iterative approach with ability to respond to issues as they arisethroughout the course of the project. In this approach, students performed a series of agile ritualssuch as showcases, retrospectives, stand-up meetings and iteration reviews.2. IntroductionThe implementation of Project-Based Learning (PBL) in science, technology, engineering, andmathematics (STEM) education has gained much interest in recent years [1-3]. PBL is a dynamicclassroom approach in which students actively explore real-world problems and acquire deepcontent understanding by taking over the
data on the extent of video viewing(coverage) of pre-class videos in three flipped undergraduate engineering courses (numericalmethods for engineers, fluid mechanics and engineering statics) as an initial step towardsimproving engagement with pre-class resources.Literature ReviewWhile the literature on flipped classes is extensive [1]-[3], studies on student engagement withpre-class materials are fewer, especially those related to viewing of pre-class videos designed toprimarily substitute (not supplement or review) traditional in-class lectures and instructor-ledproblem-solving sessions. Initial studies on engagement with pre-class videos were based onstudent self-reports that suffer from usual self-reporting biases and only recently have
hydraulic vibration machine at IIT Madras, for Indian Space Research Organization (ISRO), Tumba. In US he worked for the R&D departments of Computer, ATM and Railway Industry. He then resumed teaching at several US academic institutions. He spent two summers at NASA Kennedy Space Center as a research fellow. He received awards for academic, teaching and research excellence. His teaching experience ranges from KG to PG. After his return to India, Dr. Malladi taught his favorite subject ”Engineering Mechanics” at a few en- gineering institutions and found a need to 1. simplify the subject 2. create a new genre of class books to facilitate active reading and learning and 3. reform academic assessment for the sure
different professors taught sections EngineeringStatics in Mechanical and Aerospace Engineering with no common syllabus or commonassignments. Drop, withdraw, fail (DWF) rates varied from 2% to 78% – students picked theircourse section based on grade expectation. Over the years between 2005 and 2013, I taught moreand more of the offered sections, effectively reducing course drift and enforcing a common set oflearning objectives.Figure 1. Total Enrollment in Statics Total as taughtinby Enrollment Howard Statics, Fall and Spring Author's sections, Other faculty's
include papers discussing software tools to help students draw FBDs,papers on the assessment of FBDs, and papers on techniques to help students draw FBDs.Tools that have been developed to help students draw FBDs include an app [1], and animatedGIFs to guide students in a step-by-step procedure for drawing FBDs [2]. Free-body diagramerrors that have been reported include ones that demonstrate a misunderstanding of the physicssuch as forces drawn at the centroid [3], incorrect or missing friction forces [3, 4, 5], andincorrect direction of the weight [4, 5]. Other errors in drawing FBDs include missing arrows[6], missing axes [4], and misaligned or unlabeled vectors [7]. Davis and Lorimer [8] developeda rubric for assessing FBDs in six separate
resources, whilealso contributing to a growing body of knowledge on complex and resource-rich learningenvironments. To accomplish this goal, we have focused our efforts on understanding howstudents use a set of nine, commonly employed support resources. This list includes a variety ofdigital, physical, and collaborative resources, and all are part of students’ experiences in theFreeform environment. Table 1 below contains a brief description of each of these resourceswith citations to literature which has helped in their design or subsequent analysis. In most of our recent studies, we have examined students’ self-regulated learning usingHelp-seeking behaviors (HSB) theory as a conceptual framework19. Help-seeking behaviors referto the ways
the learning environment created by the instructor [1-2]. A properlydesigned learning environment ought to minimize the influence of the teacher on learning whilemaximizing the learning habits of the student. One potential method for doing this is to create a“specifications-based” learning environment wherein the assessment of student performance isstructured around requiring students to engage course materials in ways that are consistent witheffective learning. This paper examines the application of a specifications-based environment tothe design and delivery of a Statics/Dynamics course.The specifications-based approach outlined in this paper is derived from two disparate fields.The first is that of Statistical Process Control as practiced
coordinatesystem used [1],[2]. The idea and use of FBDs to aid in the development and solution ofmechanics problems is not new and is a standard tool in first year level mechanics course. Aliterature review into the effect of using FBDs reveals that students who drew correct FBDs weremore likely to solve problems correctly [3]-[5] and found that drawing inaccurate FBDs led tomore incorrect solutions [5] and/or led to failing the course [3]. Alternatively, other researchersnoted the opposite result; that the quality [6] or correctness [7] of the FBDs did not impactstudent performance significantly. Furthermore, similar studies noted that students who createdhigh quality FBDs were likely to produce low quality equations [8]. A potential explanation forsome
. Such an eBook providesvarious avenues for students to learn and practice concepts, and has yielded very encouragingresults, including increased student performance and positive feedback from the studentsthemselves. The presented interactive eBook has the potential to inspire other educators andcourse designers to develop and implement interactive tools in their pedagogical approach.1 - Introduction Teaching and Learning Materials (TLMs) are essential components of engineeringeducation. TLMs provide teachers with resources to deliver the course content, support studentlearning, and increase overall student success. TLMs that are offered in various formats such astext, pictures, videos, charts, and slides aid in the learning process by