Microsoft Word - fullpdf06012024 Georgian Scientists/ქართველი მეცნიერები ტ. 6 N 1, 2024 135 Georgian Scientists ქართველი მეცნიერები Vol. 6 Issue 1, 2024 https://doi.org/10.52340/gs.2024.06.01.18 By graphic method and using computer programs Determination of the location function of spherical lever mechanisms Nana Nozadze1, Prof. Mzia Kiknadze1, Davit Mania2 1Professor, Georgian Technical University; 2Student, Georgian Technical University Abstract The paper discusses the definition of the location function and graphic method for spherical mechanisms. It addresses both the analysis and synthesis tasks involved in decision-making. The proposed approach involves various geometric figures, particularly spheres, to efficiently solve movement tasks on their surfaces. This method provides a visible and less time-consuming way to determine the coordinates of separate points on spherical mechanisms. keywords: Analysis, synthesis, geometric Figure, sphere, retina, orthogonal coordinates. Introduction Geometric character Modern technical tasks solution to the majority in case Analytical methods by means of happens. despite that _ _ this time research results is accepted beforehand Given With accuracy, anyway should to note graphic for methods characteristic whole row Advantages. practice shows that _ mechanisms and tools construct to the majority cases it is possible Let's go more rationally and Effectively, if We will use it computer equipment. desired each one task when deciding Let's take advantage orthogonal Planned, something If Their use technical in the field Worker any for an engineer is available and no They are married of cadres special to prepare. It should be noted here that, using modern computer programs, it became possible to carry out kinematic and dynamic calculation and construction of mechanisms with acceptable accuracy for engineering practice. Thus, engineer - technical to the staff and various in the field working Constructors are given indefinite creative abilities tools, mechanisms and of cars research methods during selection. spherical mechanisms kinematic analysis time more difficult as an operation is considered mechanism location function Determine which _ it is possible to express only high row with equations. hard structure having mechanisms kinematic with the analysis connected tasks solution happens certain sequence With protection, theirs build and structure considering. Submitted article basic The goal is engineering for practice Acceptable research easy and visible method offer. Georgian Scientists/ქართველი მეცნიერები ტ. 6 N 1, 2024 136 Currently, the capabilities of modern computer hardware and programs allow us to solve technical tasks of any complexity based on the development of new mathematical models and to practically use any method of mechanism research with predetermined accuracy. Main part as It is known, the field on the surface located on the point sphere belonging to lots of circumference It's awesome possible _ A That's why sphere on the surface located N point to build First sphere belonging to any n circumference let's build (Fig. 1a) and then on it N point let's mark Suppose there is a center O, and two A located on the surface of a sphere of radius =1 and Point B. It is necessary to define such a point C located on the same surface that from the mentioned points the pre-given < COA and < COB will be spherically spaced. It is clear that sphere on the surface Such two point They will exist sphere of those segments bases crossing points will be whose vertices A and B is straight, while viewers Accordingly AC and BC Sections equal (Fig. 1b). fig. 1 In general, a lever mechanism with one or more degrees of movement is obtained by connecting one or more structural groups to the driving ring or rings. The sequence of conducting kinematic research and joining these groups coincides (identical). Taking them into account, we can obtain one of the well-known structural models of kinematic research of lever mechanisms using standard computer programs. The locations of the outer kinematic pairs will be known for the simplest type of two-rod groups, and the goal of the study is to determine the location of the middle kinematic pair. In this way, the location of any point in the mechanism can be found. This approach to kinematic research is valid for all types and modifications of lever mechanisms. So for example: Let's conduct a kinematic analysis of the four-ring spherical lever mechanism (Fig. 2) using purely graphic and computer software AutoCAD [1-3]. Also: 1. Kinematic diagram of spherical four-ring lever mechanism f 1 2. Generalized coordinate variation function with time In the relation f 1 = f 1 ( t ). 3. a 1, a 2, a 3, a 4, curved, curved, sided, vertical There are central corners (Fig. 2). Determine the location function of the lever mechanism ABCD f 3 = f 3 ( f 1 ) (Fig. 5). A semi-constructive diagram of the four-ring lever mechanism is given (Fig. 2). A B G Georgian Scientists/ქართველი მეცნიერები ტ. 6 N 1, 2024 137 Angles a 1, a 2, a 3, and a 4, - dimensions of the rings - function of variation of the rotation angle of the input ring - (generalized coordinate) with time = f(t) It is necessary to determine the location plan of the mechanism. fig. 2 We conduct kinematic research in the following order: 1. Let's do it unit radius having sphere Spread out. fig. 3 2. Received spread out by means of let's create two Hemispherical surface . 3. Let's cover it with the resulting surfaces, up mentioned sphere. Georgian Scientists/ქართველი მეცნიერები ტ. 6 N 1, 2024 138 4. Mark two fixed points on the surface of the sphere A and D red. 5. From point A as the center, draw a circle |AB| cord with equal radius. Let's mark one of the points B on the circle aa. 6. From one of the marked points in our case B 2 as from the center |BC| Draw an arc bb with a radius equal to the chord. 7. Similarly from point D |DC| Let's circle it with a radius equal to the chord dd arc. 8. The point of intersection of arcs b and d is the point C to be searched for. Connect points A, B, C and D with appropriate arcs. As a result, we got a plan of the locations of the mechanism in the second state. Similarly, it is possible to determine the spatial (spherical) gear points for different locations of the drive ring. The fourth figure shows spherical shape four rings Leverage mechanism private the case hook Universal joint so Cardan Mechanism. in which