ԼՐԻՎ ՄԵԽԱՆԻԿԱԿԱՆ ԷՆԵՐԳԻԱՅԻ ՓՈՓՈԽՈՒԹՅԱՆ ԹԵՈՐԵՄԻ ԵՎ ՄՈՄԵՆՏՆԵՐԻ ԿԱՆՈՆԻ ՄԵԿ ՀԱՄԱՏԵՂ ԿԻՐԱՌՈՒԹՅԱՆ ՄԱՍԻՆ / ON THE JOINT APPLICATION OF A FULL MECHANICAL ENERGY CHANGE THEOREM AND THE RULES OF MOMENTS

Աշխատանքը նվիրված է ֆիզիկայի դպրոցական դասընթացում լրիվ մեխանիկական էներգիայի փոփոխության թեորեմի և մոմենտների կանոնի հնարավոր համատեղ կիրառությունների վերհանմանըֈ Դիտարկված է կոնկրետ խնդիր, որի շրջանակում վերոգրյալ երկու կանոների կիրառման արդյունքում հնարավոր է դառնում որոշել համասեռ շրջանագծային աղեղի զանգվածի կենտրոնըֈ Խնդրի շրջանակում ստացված արդյունքն ընդհանրացվել է կամայական կենտրոնային անկյունով համասեռ շրջանաձև աղեղի համարֈ: / The work is devoted to identifying possible joint applications of the rule of moments and the theorem for changing the total mechanical energy in a school physics course. A specific problem is considered, within the framework of which, as a result of the application of the above two rules, it becomes possible to determine the center of mass of a uniform circular arc. The result obtained in the framework of the problem is generalized to a homogeneous circular arc with an arbitrary central angle.

On the Milling Strategy in Machining Curved Surfaces Based on Minimum Stress Concentration by a 3-axis Machining Center

3-axis computer numerical control machining centers are used in machining due to their simple operation. When machining curved surfaces, the 3-axis CNC machining centers use interpolation lines segment to fit the curved surfaces. The quality of the machined surface is affected by the length of the interpolation line segment. Sharp corners are formed at the junction of straight segments. The appearance of sharp corners will lead to increased stress concentration. To study the relationship between surface quality and interpolation straight line in surface processing, this paper establishes the mathematical model of surface topography in 3-axis ball-end milling curved surfaces based on the acceleration and deceleration control. Based on the surface topography model, the surfaces stress concentration factor analysis is carried out in machining curved surfaces with variable curvatures with different lengths of interpolation lines. The results show that when the length of interpolation lines and the radius of curvature are kept constant, the stress concentration factor decreases with the increase of the central angle. When the length of the interpolation lines and the central angle are kept constant, the stress concentration factor decreases with the increase of the radius of curvature. When the radius of curvature and the central angle are kept constant, the stress concentration factor increases as the length of the interpolation lines increases. A method of selecting the length of interpolation lines based on the surface’s stress concentration is proposed. Through the optimization of the tool path, the quality of the machined surfaces can be improved.

PENGEMBANGAN BAHAN AJAR INTERAKTIF UNTUK PEROLEHAN KETERAMPILAN PADA MATERI LINGKARAN

This research aims to determine the feasibility of interactive teaching materials that are developed, and how intellectual skills of students after using teaching materials that are developed. The research method used is descriptive. The subjects of this research were 24 students from class XI SMP Islam Bawari Pontianak. The data source of this research were the student test answers sheet, and the validation sheet for the feasibility of interactive teaching materials. The results showed that interactive teaching materials were declared to be very valid, refer to material experts and media experts. The students' intellectual skills of relationship the central angle with length of arc is 58.33% in the sufficient category. The students' intellectual skills of relationship the central angle with area of circle sector is 50% in the sufficient category. The students' intellectual skills of solve problems related to the central angle, inscribed angle, length of arc, and area of circle sector, and its relationship is 20.83% in the low category.Keywords: Circles, Intellectual Skills, Interactive Teaching Materials

Surfaces of congruent sections on cylinders

Introduction. The definition of surfaces of congruent sections was first formulated in the work written by I.I. Kotov. These and several other types of surfaces, generated by the motion of a curve, belonged to the class of kinematic surfaces. Such kinematic surfaces as those of plane parallel displacement, surfaces of rotation, Monge surfaces, cyclic surfaces with ge-nerating circles having constant radius, rotative and spiroidal surfaces, helical some helix-shaped surfaces can be included into the class of surfaces that have congruent sections. Materials and methods. Using I.I. Kotov’s methodology, the authors first derived parametrical and vector equations for eight surfaces of congruent pendulum type cross sections of circular, elliptic, and parabolic cylinders and several helix-shaped surfaces. Circles, ellipses, and parabolas, located in the plane of the generating curve of a guiding cylinder or in the planes of a bundle that passes through the longitudinal axis of a cylinder, generate plane curves. Ellipses, analyzed in the article, can be easily converted into circles and this procedure can increase the number of shapes analyzed here. Results. Formulas are provided in the generalized form, so the shape of a plane generating curve can be arbitrary. Some surfaces of congruent sections are determined by two varieties of parametric equations. In one case, the central angle of the guiding cylindrical surface was used as an independent parameter, but in the other case, one of rectangular coordinates of the cylinder’s guiding curve served as an independent parameter. Two types of surfaces are analyzed: 1) when local axes of generating curves remain parallel in motion; 2) when these axes rotate. Conclusions. The analysis of the sources and the results, recommendations and proposals for application of surfaces, having congruent sections, is made with a view to their use in architecture and technology. The list of references has 27 positions, and it shows that the surfaces considered in this paper are being analyzed by architects, engineers, and geometricians both in Russia and abroad.

Simulation of centroids of non-circular wheels with internal and external rolling from arcs of symmetrical curves

The article considers the design of noncircular wheels, which serve as centroids in the design of gears. Centroids consist of congruent arcs of a given symmetric curve. The number of these arcs, that is the elements of the centroid, is determined by the type of gearing (internal or external). In external gearing, the number of elements of both centroids can be arbitrary, starting with one element. In the case of internal gearing, the number of elements of the internal centroid must be one less than the number of elements of the external centroid. If the number of elements is the same, then the centroids coincide. Rolling centroids one by one occurs in the absence of sliding. This is possible provided that the lengths of the arcs of the individual elements of both centroids are equal to each other. The construction of a centroid is carried out in a polar coordinate system. Both centroids are formed by rotating its element, that is the arc of the curve, at a given angle around the pole. The magnitude of the angle depends on the number of elements of the centroid. When rolling one centroid on the other, the pole of the moving centroid must describe the circle. In this case, the rolling of a moving centroid on a stationary one can be replaced by the rotational motion of both centroids around the fixed centers (poles). The point of contact of the centroids during their rotation is on the segment connecting the centers of rotation and which is called the center-to-center distance. This point for non-circular wheels when they rotate makes a certain movement along the specified segment, and for round wheels remains stationary. The length of the arc of an element of one centroid is determined by the magnitude of the central angle on which it rests. The same applies to the element of the second centroid. If the lengths of the arcs of the elements of the centroid are equal, then the values of the corresponding angles are not equal and are in a certain functional dependence. Finding this dependence is reduced to the integration of the expression obtained on the basis of the equality of the differentials of the arcs of the corresponding centroid elements. This expression may not be integrated for all curves from which the arcs of the original or leading centroid are formed. If the expression cannot be integrated, then the construction of the driven centroid must be carried out by numerical methods. The article considers a curve based on the hyperbolic cosine, for which the obtained expression is integrated. The parametric equations of the curves of which the arcs of both the leading and the driven centroids consist are given. It is shown that for a centroid with a given ratio of elements the intercenter distance is determined unambiguously. Centroid drawings with different number of elements for internal and external gearing are constructed.

Numerical Study on Shear Performance of a New Perfobond Connector with Controllable Stiffness

To improve the shear behavior and design applicability of rubber ring perfobond connectors (RPBLs), a new rubber ring that aims to make the shear stiffness of RPBLs controllable was proposed. Firstly, the conceptual design and configuration of the new rubber rings were presented and discussed. Subsequently, finite element (FE) models for modified push-out tests of new RPBLs were established based on the validated modeling method. The initial shear stiffness is dominated by the horizontal projected contact area between hole walls and concrete dowels. γ is defined as the ratio of the horizontal projected length of hollows to the diameter of holes. The shear stiffness of new RPBLs is about 35%, 60%, and 82% of the shear stiffness of PBLs when γ equals 0.25, 0.5, and 0.75, respectively. Employing the new rubber rings with varying central angles on conventional PBLs is feasible to obtain the required stiffness for RPBLs. Further, the effects of the number of sectors, the size of side wings, the central angle of hollows, the offset angle, and the thickness of rubber rings were analysed. Based on the numerical results, the proper thickness of side wings is no larger than 2 mm. The thicker side wing could reduce the confinement effects provided by surrounding concrete on concrete dowels, resulting in a drop of the yield load of new RPBLs. The number of sectors is suggested to be no less than 6 so that the shear behavior of new RPBLs is irrelevant to the offset angle. Besides, the shear stiffness is not related to the thickness of rubber rings. To improve the yield load of RPBLs and obtain the moderate recovered stiffness, the thickness of rubber rings is recommended as 2 mm. Finally, the expression for the shear stiffness of new RPBLs was proposed.

Analysis of Learning Obstacles of Junior High School Students on The Topic of Circle

Geometry is one of the subjects in mathematics school that is important to learn, because through geometry, almost every daily problem can be solved. However, the achievements of Indonesian students in the field of geometry are still relatively low. This study aims to identify the possibility of students' learning obstacles in one area of geometry, which is circle subject. The method used in this study was qualitative research method with survey-based research design, involved 30 eight-grade students from a junior high school in Bandung. The data were collected by triangulation method using an instrument test consisting of tests of students mathematical comprehension ability that is related to circle subject, and the non-test instruments used consist of collection of observations, guidelines for student interviews, and study documents. Results showed that there were identified any types of learning obstacle caused by epistemological obstacle among others (1) learning obstacle related to the concept of sector caused by an error in the perspective of students, (2) learning obstacle related to the form of geometrical representation from the central angle of the circle caused by the student's limited knowledge of the central angle and chord of the circle. In addition, also found types of learning obstacle caused by didactical obstacle, among others (1) learning obstacle related to communication skills in presenting the definition of sector concept caused by not creating discussion and presentation activities when learning takes place, and (2) learning obstacle related the concept of the relationship between the diameter with chord of the circle caused by the presentation of material that is less detailed either provided by the teacher or presented in the source book used.

Pengembangan Bahan Ajar Berbasis Penalaran pada Materi Sudut Pusat dan Sudut Keliling Lingkaran

Reasoning based research generally examines the application of learning models or learning methods. So far, there are still rarely studies that examine the use of teaching materials to improve the quality of learning. This study aims to develop teaching materials related to the central angle and the circumference of the circle based on reasoning. The development model used is the ADDIE development model, namely Analysis, Design, Development, Implementation and Evaluation. The analysis was conducted by involving students of SMPN 1 Kabila as research subjects. The results showed the quality of teaching materials was declared valid with a percentage of 75%. Practicality of teaching materials based on the results of student questionnaire responses reached very good categories with a percentage of 82.82%. This shows that reasoning based teaching materials can be used in the learning process. Abstrak:Penelitian berbasis penalaran umumnya mengkaji tentang penerapan model atau metode pembelajaran. Sejauh ini, masih jarang penelitian yang mengkaji tentang penggunaan bahan ajar untuk meningkatkan kualitas pembelajaran. Penelitian ini bertujuan untuk mengembangkan bahan ajar materi hubungan sudut pusat dan sudut keliling lingkaran berbasis penalaran. Model pengembangan yang digunakan adalah Model pengembangan ADDIE, yaitu Analysis (Analisis), Design (Desain), Development (Pengembangan), Implementation (Implementasi) dan Evaluation (Evaluasi). Analisis dilakukan dengan melibatkan siswa SMPN 1 Kabila sebagai subjek penelitian. Hasil penelitian menunjukan kualitas bahan ajar dinyatakan valid dengan persentase 75%. Kepraktisan bahan ajar berdasarkan hasil angket respon siswa mencapai kategori sangat baik dengan persentase 82,82%. Hal ini menunjukkan bahwa bahan ajar berbasis penalaran dapat digunakan dalam proses pembelajaran.