Synthesis of Five-bar Motion Generation with Gear Train Fabrication Tolerances (original) (raw)
Related papers
On the kinematics and synthesis of a geared five-bar slider–crank mechanism
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2011
The geared five-bar mechanism possesses kinematic abilities that qualify its utility in various industrial applications. Small changes to the mechanism topology or dimensions create new designs with different motion characteristics. This article presents design-orientated kinematical insights and mathematical treatments for the embodiment of the mechanism in which the end gear is eccentrically pivoted to a sliding element. For its synthesis, a kinematic classification is introduced and approximate curves are used to guide the motion of the slider. A gradient-based Levenberg–Marquardt formulation is employed for the optimization procedure. Geometric, mobility, and dimensional constraints are utilized together with numerical position equations for the analysis. Two case studies are presented at the end of this article to highlight the versatility of the mechanism and prove the validity of the presented mathematical model.
On the Kinematics and Synthesis of the Geared Five-Bar Slider-Crank Mechanism
The geared five-bar mechanism possesses kinematic abilities which qualify it for use in various industrial applications. Small changes to the mechanism topology or dimensions create new designs with different motion characteristics. This paper presents designorientated kinematical insights and mathematical treatments for the embodiment of the mechanism in which the end gear is eccentrically pivoted to a sliding element. For the synthesis effort, a kinematic classification will be introduced and approximate curves will be used to guide the motion of the slider. A gradient-based Levenberg-Marquardt formulation will be employed for the optimisation procedure. Geometric, mobility and dimensional constraints will be utilised together with numerical position equations for the analysis. Two case studies are presented at the end of the paper to highlight the versatility of the mechanism and prove the validity of the presented mathematical model.
Synthesis of Four-bar Motion Generation Considering Worst Case Joint Tolerances
2011
Abstract— Four-bar motion generation is used to synthesize a mechanism which passes through or approximate prescribed rigid-body positions. This work will discuss the motion generation of four-bar mechanism with position tolerance variations due to joint running clearance. The tolerance variations study will be based on the standards of American National Standard Institute (ANSI). The new design constraint introduced in this paper will consider the joint tolerances and incorporate it into the displacement position matrix of coupler points described in the conventional planar four-bar motion generation models. The synthesized planar four-bar mechanism will produce tolerance limits for moving pivots and link length from which any mechanism can be synthesized to satisfy the prescribed coupler points with their prescribed tolerances. The included example demonstrates the synthesis of a four-bar mechanism with joint tolerances. 1
Optimized five-bar linkages with non-circular gears for exact path generation
Mechanism and Machine Theory, 2009
In this paper, a five-bar linkage with non-circular gears is proposed as a mechanism capable of precisely moving a coupler point along a prescribed trajectory. The first step of the proposed methodology is the inverse kinematic analysis of the linkage, whose mobility, without geared bodies, is two. Therefore, by imposing the required configuration of the coupler at any instant, the rotation of the two inputs is evaluated. A pair of non-circular gears is then synthesized on the basis of the relation between these two angular inputs, thus reducing the mobility to one. The final combined mechanism is able to exactly perform a specific task of path generation. In the design of non-circular gears, a basic requirement is that the non-circularity of the pitch curves is kept as low as possible. Such non-circularity affects both the feasibility of gear manufacture and the dynamic behaviour of the output non-circular gear. For this reason, an optimization of the five-bar linkage with non-circular gears is also proposed, by defining the objective function on the basis of proper dimensional and kinematic criteria. A penalty method is used to manage a set of constraints to which both the linkage and the gears are subjected, while a genetic algorithm is employed to search for a global optimum solution.
GIS Journal, 2021
For the current world population, there is a heavy demand to supply the accommodates needed for peoples for leading a comfortable life. To fulfill these requirements, industries have to focus on improving the capacity of machinery with better-advanced technologies which can perform multiple tasks within a stipulated time with less space. So mechanisms play a vital role in doing that. The determination of position and lengths of each link associated with mechanisms are known as the synthesis of mechanisms. It is very easy when the mechanism is of single degrees of freedom (DOF) and many techniques are available for that. But the mechanism with only a single DOF and with only lower pairs is unable to meet the requirement of industries. Hence higher DOF mechanisms with higher paired mechanisms are more encouraging nowadays. So there is a scope for the synthesis of these types of mechanisms. Hence in this paper author has focused on the synthesis of two DOF offset slider mechanisms with variable topology methods and it can be achievable with fewer iterations. The variable topology method is an analytical method in which complex numbers are used for the synthesis process. The author has tried to reduce the solution space by considering the geometrical and operational parameters of links.
This article presents the synthesis of an in-line ten link gear slider mechanism of variable topology type for two finitely separated positions. The synthesis is carried out in two phases, considering in-line ten link gear slider mechanism as in-line nine link gear slider mechanism in each phase. Motion generation, one of the tasks of kinematic synthesis is the design criterion. This process is illustrated with an example. The synthesized mechanism comprises of 12-revolute, 1-gear and 1-slider joint. Thus, variable topology method focuses on a noniterative and simplified way of mechanism synthesis.
Analysis and Synthesis of Mechanisms with Bars and Gears Used in Robots and Manipulators
SSRN Electronic Journal, 2017
Bars and gears are used everywhere today, but a wide range of uses is robotics and mechatronics. Since ancient times, automations and mechanization have been used with mechanisms consisting of chains of bars and gears. These were obviously used for the purpose of transmitting the movement and its transformation, that is to say, as a mechanical transmission. Gear and bar automation are used today as modern mechanical transmissions, serial and parallel robots, machine building industry and all industrial areas where automation has penetrated. In fact, robotic gears and gears are the basis for mechanical transmissions to robots and at the same time have other roles such as balancing, support, etc. The most commonly used gears are tapered, conical gears, because they work faster, more dynamically, occupy less space, have fewer toothed gear teeth, low volume, light movement different directions and a multitude of features that make them irreplaceable within mobile mechanical systems. The gears and gears are increasingly used in the construction of manipulators and industrial robots, especially in the MOr. In the kinematic openings of Positioning Mechanisms (MPz) of the robots, also referred to as trajectory generators, a first kinematic chain with bars is attached, to which is attached a kinematic chain with cylindrical, conical and hypoid gears. The mechanical chains that can be made of conical mechanical transmissions and bars are complex, extremely complex and can work on different spaces and axes, with inclines and directional changes as desired. From this point of view, they can't be replaced by other types of mechanical mechanisms or transmissions. A complex kinematic scheme with bevel gears and conical gears of a manipulator-robot with 6 + 1 mobilities is analyzed, where the positioning mechanism (RRR) is not distinguishable from the RRR orientation mechanism. The two kinematic chains of MPz (RzRxxRx) and MOr (RzRxRxRz) are staged (in extension). At the end (O6 point) of the articulated chain O0O1O2O3O4O5 the gripping mechanism (MAp), made with two articulated parallelograms, is attached. All 6 + 1 kinematic chains are operated by means of worm gear reducers with electric motors located at the base. The kinematic chain with bars is simplified to the left of Fig. 1 and to the right is an axial projection of the complete kinematic scheme of the gear with gears and gears. The articulated bars (0, 1, 2, 3, 4, 5, 6) with six movable elements are the main kinematic chain to which are attached six kinematic chains with conical gears.
Kinematic analysis and synthesis of an adjustable six-bar linkage
Mechanism and Machine Theory, 2009
This paper investigates the kinematics of an adjustable six-bar linkage where the rotation of the input crank is converted into the oscillation of the output link. This single-degree-of freedom planar linkage will be used as a variable-speed transmission mechanism where the input crank rotates at a constant speed and the output link consists of an overrunning clutch mounted on the output shaft. The analysis uses a novel technique in which kinematic coefficients are obtained with respect to an independent variable. Then kinematic inversion is used to express the kinematic coefficients with respect to the input variable of the linkage. This technique decouples the position equations and provides additional insight into the geometry of the adjustable linkage. The angle through which the output link oscillates, for each revolution of the input crank, can be adjusted by a control arm. This arm allows a fixed pivot to be temporarily released and moved along a circular arc about a permanent ground pivot. The paper shows how to determine the angle of oscillation of the output link for a specified position of the fixed pivot and investigates the extreme positions of the output link corresponding to the extreme positions of a point on the coupler link. For this reason, the paper includes a study of the geometry of the path traced by a coupler point and determines the location of the ground pivot of the control arm which will cause the output link to remain stationary during a complete rotation of the input crank. Finally, the paper shows how the kinematic analysis results can be used, in a straightforward manner, to redesign the control arm.
Two FSP Synthesis of Eight Link Gear Mechanism for Motion Generation with 9R-1G Joints
International Journal of Engineering Applied Sciences and Technology
The paper presents a mechanism consisting of nine revolute and one gear joints. A planar eight link gear mechanism having two degrees of freedom is considered for synthesis using variable topology method operating in two phases for the task of motion generation. Complex number method is presented as an ideal tool for synthesizing the linkage. Seven link gear mechanism is considered as a portion of eight link gear mechanism in each phase and illustrated with an example. These seven link gear mechanism portions of eight link gear mechanism are designed for two finitely separated positions. Variable topology method focuses on a non-iterative and simplified way of mechanism synthesis.
2010
The paper presents an analytical method to synthesize a seven-bar slider mechanism with variable topology for motion between two dead-center positions. Synthesis is carried out in two phases for motion generation between two dead-center positions. The tasks like path generation with prescribed timing and function generation are also dealt with. A dyadic complex number method is used. The complexity nature of synthesis of multi-degree freedom mechanisms made simpler through variable topology operating in two phases. The general attractions of the method are simplicity, ease of operation, easy to understand, codable for programming etc.