Introduction of New Concepts and Problem Solving in Engineering Dynamics

2007 ◽  
Author(s):  
Serge Abrate
Keyword(s):  
Problem Solving ◽  
Concept Maps ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
New Concepts ◽  
Body Dynamics ◽  
Basic Equations ◽  
And Mathematics ◽  
Work Done

A survey of a large number of well-known textbooks for an undergraduate dynamics class showed that often new concepts are introduced without a clear connection to previously discussed material. For example, the concepts of work done by a force, linear momentum, angular momentum, and power are often introduced without a clear direct connection to Newton’s law. Similarly, in rigid body dynamics, important concepts such as the center of mass and the moments of inertia of the body are often introduced with little or no background. This article shows how all the important concepts in dynamics flow directly and logically from Newton’s laws. This is done through simple direct derivations. Connections are made clear by concept maps that help students understand how these different concepts are related. In addition to introducing new concepts and deriving some of the basic equations, a dynamics class should also introduce students to problem solving help them develop a systematic approach. This article describes a five step approach that is recommended for both high context and low context problems. In that context we stress that problem solving is a process that involves the application of known concepts and mathematics.

The Forced Oscillations of Submerged Bodies

2003 ◽  
Vol 125 (4) ◽  
pp. 710-715
Author(s):  
Angel Sanz-Andre´s ◽  
Gonzalo Tevar ◽  
Francisco-Javier Rivas
Keyword(s):  
Rigid Body ◽  
Small Amplitude ◽  
Center Of Mass ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Central Point ◽  
Modal Testing ◽  
Forced Oscillations ◽  
Motion Equations ◽  
Marine Applications

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.

Rigid Body Dynamics, Constraints, and Inverses

2005 ◽  
Vol 74 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Hooshang Hemami ◽  
Bostwick F. Wyman
Keyword(s):  
Rigid Body ◽  
State Space ◽  
Tracking Error ◽  
Feedback System ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Contact Forces ◽  
Constraint Forces ◽  
Inverse Systems ◽  
Body Dynamics

Rigid body dynamics are traditionally formulated by Lagrangian or Newton-Euler methods. A particular state space form using Euler angles and angular velocities expressed in the body coordinate system is employed here to address constrained rigid body dynamics. We study gliding and rolling, and we develop inverse systems for estimation of internal and contact forces of constraint. A primitive approximation of biped locomotion serves as a motivation for this work. A class of constraints is formulated in this state space. Rolling and gliding are common in contact sports, in interaction of humans and robots with their environment where one surface makes contact with another surface, and at skeletal joints in living systems. This formulation of constraints is important for control purposes. The estimation of applied and constraint forces and torques at the joints of natural and robotic systems is a challenge. Direct and indirect measurement methods involving a combination of kinematic data and computation are discussed. The basic methodology is developed for one single rigid body for simplicity, brevity, and precision. Computer simulations are presented to demonstrate the feasibility and effectiveness of the approaches presented. The methodology can be applied to a multilink model of bipedal systems where natural and/or artificial connectors and actuators are modeled. Estimation of the forces is accomplished by the inverse of the nonlinear plant designed by using a robust high gain feedback system. The inverse is shown to be stable, and bounds on the tracking error are developed. Lyapunov stability methods are used to establish global stability of the inverse system.

scholarly journals PENINGKATAN MINAT DAN HASIL BELAJAR BILANGAN BERPANGKAT DAN BENTUK AKAR SISWA KELAS X TEKNIK SEPEDA MOTOR SMK ELEKTRO SIJUNJUNG DENGAN MENGGUNAKAN PETA KONSEP

2019 ◽  
Vol 2 (1) ◽  
pp. 51
Author(s):  
Dewi Sefriyanti
Keyword(s):  
Concept Maps ◽  
Mathematics Learning ◽  
Meaningful Learning ◽  
New Concepts ◽  
Inclusive Concept ◽  
The Subject ◽  
Basic Concepts ◽  
And Mathematics ◽  
The Relationship ◽  
Hierarchical Manner

This study aims to increase students' interest and mathematics learning achievements on the subject of rank numbers, root shapes and logarithms. In this study I used a concept map. Concept maps are a tool in the form of a scheme that states the relationship between concepts starting from the general to the specific ones which are connected through arrows in the form of propositions. Proposition is two or more statements about a concept that are related to words or arrows. Concept maps play an important role in meaningful learning, with concept maps of students being trained to think, in students being asked to think about concepts or events they already know. Meaningful learning is easier to take place if new concepts are linked to concepts that are inclusive, inclusive concepts that are basic concepts that are more general in nature. Concept maps must be arranged in a hierarchical manner, which means that a more inclusive concept is at the top of the map, the concepts below are sorted into less inclusive ones.

Design of a Compliant Jumping Robot With Passive Stabilizer

2020 ◽  
Author(s):  
Joshua Hooper ◽  
Martin Garcia ◽  
Paul Pena ◽  
Ayse Tekes
Keyword(s):  
Center Of Mass ◽  
Vertical Plane ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Main Body ◽  
Body Parts ◽  
Element Analysis ◽  
Flexure Hinges ◽  
Jumping Robot ◽  
The Impact

Abstract This study presents the design and development of a compliant multi-link hopping mechanism actuated by a single DC motor. Two main design goals are to have a single piece designed main body for the jumping robot and a passive stabilizer to allow consecutive jumps. Mechanism consists of monolithically designed large deflecting main body incorporating the gears and initially curved flexure hinge. Due to the limitations of the design goal, revolute motion between top and bottom legs on the main body are realized by a compliant link which replaces the need of ball bearings. Also, continuous energy store and release during jumping is ensured by the same flexure hinges. Passive self-righting cage is attached to the bottom of the main body to maintain upright position both in landing and takeoff. The cage allows the center of mass to stay in the vertical plane to prevent tilting. During landing, cage absorbs the impact and allows the main body to roll to its initial configuration so that the robot can complete jumping. Mechanism parts including the cage are 3D printed using PETG. Design optimization of the body parts including the rigid legs and flexure hinges are analyzed both experimentally and analytically. Finite element analysis is performed to calculate the equivalent stiffness and natural frequency of the jumping robot and simplified mathematical model is derived using rigid body dynamics.

Mechanical work in terrestrial locomotion: two basic mechanisms for minimizing energy expenditure

1977 ◽  
Vol 233 (5) ◽  
pp. R243-R261 ◽  
Author(s):  
G. A. Cavagna ◽  
N. C. Heglund ◽  
C. R. Taylor
Keyword(s):  
Center Of Mass ◽  
Forward Direction ◽  
Gravitational Energy ◽  
The Body ◽  
Unit Weight ◽  
Gravitational Potential Energy ◽  
Terrestrial Locomotion ◽  
Energy Conserving ◽  
Walking Speeds ◽  
Work Done

The work done during each step to lift and to reaccelerate (in the forward direction) and center of mass has been measured during locomotion in bipeds (rhea and turkey), quadrupeds (dogs, stump-tailed macaques, and ram), and hoppers (kangaroo and springhare). Walking, in all animals (as in man), involves an alternate transfer between gravitational-potential energy and kinetic energy within each stride (as takes place in a pendulum). This transfer is greatest at intermediate walking speeds and can account for up to 70% of the total energy changes taking place within a stride, leaving only 30% to be supplied by muscles. No kinetic-gravitational energy transfer takes place during running, hopping, and trotting, but energy is conserved by another mechanism: an elastic “bounce” of the body. Galloping animals utilize a combination of these two energy-conserving mechanisms. During running, trotting, hopping, and galloping, 1) the power per unit weight required to maintain the forward speed of the center of mass is almost the same in all the species studied; 2) the power per unit weight required to lift the center of mass is almost independent of speed; and 3) the sum of these two powers is almost a linear function of speed.

Dynamics of Flexible Body Negotiating a Curve

2016 ◽  
Vol 11 (4) ◽  
Author(s):  
Huailong Shi ◽  
Liang Wang ◽  
Ahmed A. Shabana
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Flexible Body ◽  
Motion Trajectory ◽  
Centrifugal Forces ◽  
Coriolis Forces ◽  
Body Dynamics ◽  
Body Reference

When a rigid body negotiates a curve, the centrifugal force takes a simple form which is function of the body mass, forward velocity, and the radius of curvature of the curve. In this simple case of rigid body dynamics, curve negotiation does not lead to Coriolis forces. In the case of a flexible body negotiating a curve, on the other hand, the inertia of the body becomes function of the deformation, curve negotiations lead to Coriolis forces, and the expression for the deformation-dependent centrifugal forces becomes more complex. In this paper, the nonlinear constrained dynamic equations of motion of a flexible body negotiating a circular curve are used to develop a systematic procedure for the calculation of the centrifugal forces during curve negotiations. The floating frame of reference (FFR) formulation is used to describe the body deformation and define the nonlinear centrifugal and Coriolis forces. The algebraic constraint equations which define the motion trajectory along the curve are formulated in terms of the body reference and elastic coordinates. It is shown in this paper how these algebraic motion trajectory constraint equations can be used to define the constraint forces that lead to a systematic definition of the resultant centrifugal force in the case of curve negotiations. The embedding technique is used to eliminate the dependent variables and define the equations of motion in terms of the system degrees of freedom. As demonstrated in this paper, the motion trajectory constraints lead to constant generalized forces associated with the elastic coordinates, and as a consequence, the elastic velocities and accelerations approach zero in the steady state. It is also shown that if the motion trajectory constraints are imposed on the coordinates of a flexible body reference that satisfies the mean-axis conditions, the centrifugal forces take the same form as in the case of rigid body dynamics. The resulting flexible body dynamic equations can be solved numerically in order to obtain the body coordinates and evaluate numerically the constraint and centrifugal forces. The results obtained for a flexible body negotiating a circular curve are compared with the results obtained for the rigid body in order to have a better understanding of the effect of the deformation on the centrifugal forces and the overall dynamics of the body.

On Singularity of Rigid-Body Dynamics Using Quaternion-Based Models

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Homin Choi ◽  
Bingen Yang
Keyword(s):  
Dynamic Response ◽  
Rigid Body ◽  
Dynamic Modeling ◽  
Degrees Of Freedom ◽  
Rigid Bodies ◽  
Rigid Body Dynamics ◽  
The Body ◽  
Applied Torque ◽  
Body Dynamics

It is well known that use of quaternions in dynamic modeling of rigid bodies can avoid the singularity due to Euler rotations. This paper shows that the dynamic response of a rigid body modeled by quaternions may become unbounded when a torque is applied to the body. A theorem is derived, relating the singularity to the axes of the rotation and applied torque, and to the degrees of freedom of the body in rotation. To avoid such singularity, a method of equivalent couples is proposed.

A new definition of mechanical work done in human movement

1979 ◽  
Vol 46 (1) ◽  
pp. 79-83 ◽  
Author(s):  
D. A. Winter
Keyword(s):  
Center Of Mass ◽  
Human Movement ◽  
Ground Level ◽  
The Body ◽  
Biomechanical Analysis ◽  
Major Purpose ◽  
External Work ◽  
Internal Work ◽  
Definition Of ◽  
Work Done

The definition of efficiency of human movement has often been unable to cope with activities such as level gait because the numerator of the efficiency equation includes only external work done by the body on an external load. The major purpose of this paper is to propose a definition that not only accounts for any external work but also the internal work done by the limbs themselves. The internal work involves a new biomechanical analysis that takes into account all potential and kinetic energy components, all exchanges of energy within and between segments, and both positive and negative work done by the muscles. This analysis was applied to a study of over-ground level gait on eight subjects walking at different walking speeds. The internal work/stride as calculated from the sum of segment energies was compared with the same calculation on the body's center of mass energy. The latter was found to be in error (low) by 16.2% and could be low by as much as 40%. The average internal work per body mass per distance walked was 1.09 J/kg.m.

scholarly journals Identifying Exceptional Talent in Science, Technology, Engineering, and Mathematics: Increasing Diversity and Assessing Creative Problem-Solving

2020 ◽  
Vol 31 (3) ◽  
pp. 161-210 ◽  
Author(s):  
C. June Maker
Keyword(s):  
Problem Solving ◽  
Concept Maps ◽  
Mathematical Problem ◽  
The United States ◽  
Creative Problem Solving ◽  
Grade Point ◽  
Level Of Education ◽  
Science Technology ◽  
Creative Problem ◽  
And Mathematics

In the Cultivating Diverse Talent in STEM project, funded by the National Science Foundation in the United States, new assessments were developed, field tested, used to identify students with exceptional talent in science, technology, engineering, and mathematics (STEM), and compared with existing methods (grade point average [GPA], letters of recommendation, self-statements). Students identified by both methods participated in an internship program in laboratories of scientists on the campus of an R1 university in the Southwest. Existing methods limited the diversity of students identified. Significant differences were found between students identified by the new methods (M2) and existing methods (M1) in GPA, ethnicity, and parent level of education. Ethnicity differences may be due to the ethnic makeup of the partner schools, but differences in GPA and parent level of education cannot be attributed to the location of schools. Although GPAs of M1 students were significantly higher (3.71) than those of M2 students (3.07) and M1 students came from higher income groups and schools in higher income areas, the M2 students scored higher on all the performance assessments of creative problem-solving and at similar levels on concept maps and mathematical problem-solving. Studies of the usefulness and psychometric properties of the new assessments are needed with different groups and in different contexts.

Pengaruh Penerapan Strategi Pemecahan Masalah dalam Pembelajaran Kooperatif Pendekatan Struktural Think Pair Share (TPS) Terhadap Hasil Belajar Matematika Siswa Kelas VIII SMP Negeri 14 Pekanbaru

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Atma Murni ◽  
Rini Dian Anggraini ◽  
Sakur
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Research Design ◽  
Mathematics Learning ◽  
Learning Outcome ◽  
Structural Approach ◽  
Comparison Research ◽  
And Mathematics ◽  
Problem Solving Strategy ◽  
Solving Strategy

Tujuan dari penelitian ini adalah untuk mengetahui pengaruh penerapan Strategi Pemecahan Masalah dalam pembelajaran kooperatif pendekatan struktural Think Pair Share (TPS) terhadap hasil belajar matematika siswa kelas VIII SMP Negeri 14 Pekanbaru. Penelitian ini menggunakan desain penelitian pra eksperimental menggunakan desain penelitian perbandingan kelompok statis. Instrumen pengumpulan data meliputi tes keterampilan mahematika awal dan tes hasil belajar matematika. Data dianalisis menggunakan uji t. Hasil penelitian ini menunjukkan bahwa terdapat pengaruh strategi pemecahan masalah dalam pembelajaran kooperatif pendekatan struktural Think Pair Share (TPS) terhadap hasil belajar matematika siswa kelas VIII SMP Negeri 14 Pekanbaru.   The aim of this study was to know the influence of Problem Solving Strategy implementation in cooperative learning of structural approach Think Pair Share (TPS) to mathematics learning outcome of VIII class students of SMP Negeri 14 Pekanbaru. This study use pre experimental research design using The static group comparison research design. The instruments of  data collection include early mahematics skills test and mathematics learning outcome test. Data were analyzed using t test. The result of this study showed that there is influence of problem solving strategy in cooperative learning of structural approach Think Pair Share (TPS)  to mathematics learning outcome  of  VIII class students of SMP Negeri 14 Pekanbaru

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