Compile a table of 1 dof spatial mechanisms having 2 3 and. The construction of a spatial mechanism is amazingly versatile. Feasible configurations of compliant rssr mechanism were enumerated. By mathematical modeling and algorithms, relationship formula of motion parameters is set up and the solutions of angular displacement, angular velocity and angular acceleration are obtained.
The purpose of this thesis is to provide a complete package for the synthesis and design of the rssr spatial function. Dynamic analysis of a selected spatial onedof linkage. For this purpose, the dimensions to make zero coefficients of trigonometric terms in the expression of transmission angle, are obtained. By utilizing the passive degree of freedom of the coupler of the rssr mechanism and its design equations 2,3, the design equations for the remaining cs link of the rssrsc mechanism were developed using spatial transformation matrices under the constant length and orthogonality constraints of. Many other uses are possible, but these have not been developed because of the lack of a unified theory. An experimental rssr crank and rocker mechanism has been devised and manufactured to facilitate the dynamic investigation of the input and output torques present, the force components acting in the link members and at the joints of the machine under various loading conditions, for a. Aiming at the complexity of kinetic analysis of spatial mechanism by analytical method, an analysis model is established in 3d cartesian coordinate system.
Application to general spatial fourbar, planar slidercrank final examination applications include rccc, rssr, rssp, robotic manipulators, etc. Spatial rssr mechanism design by graphics method based on 3d. Synthesis and design of the rssr spatial mechanism for. The rssr mechanism may be used in place of a pair of bevel gears between two shafts in space 2. Besides these methods enable the designer to benefit the advantages of the algebra of exponential rotation matrices. Kinzel 599 kinematic analysis and synthesis of type iii movable spatial 6r mechanism with three adjacent parallel axes chungching lee and hongsen yan 607. Shaking forces of the mechanism on all four plans 10 in this paper, the method used for balancing is the addition of two counterweights on disks 2 and 3. Mechanisms can be divided into planar mechanisms and spatial mechanisms, according to the relative motion of the rigid bodies. Pdf synthesis of the optimal rssr mechanism for the motion. The spatial fourbar mechanism treated in this paper for revolutesphericalsphericalrevolute joint in the order given. Kinematics analysis and optimization of carbonfree vehicle of 8shaped trajectory based on spatial rssr mechanism figure 1. Alkesh used the whitworth mechanism to constructing a high velocity impacting press.
It consists of four bodies, called bars or links, connected in a loop by four joints. Study on the condition of crank of spatial fourbar linkagej. By normalizing these with respect to a 1, a design chart is presented. In view of the low stability of the carbonfree trolley based on the spatial rssr mechanism, the equivalent plane mechanism method is used to analyze the spatial rssr mechanism and the motion analysis of its driving mechanism is carried out. One strategy to suppress the resulting frame vibration is to reduce these forces and moments by adding counterweights to. Generally, the joints are configured so the links move in parallel planes, and the assembly is called a planar fourbar linkage. Revolutespherical, sphericalrevolute rssr mechanisms are simple devices used to obtain inputoutput relations with prescribed spatial orientations of motion axes. In the binding line,clamp forming is finished by the spatial rssr mechanism of the unto playing institutions. Spherical and spatial fourbar linkages also exist and are used in practice. Complex number method for kinematic analysis of spatial. Kinematic analysis on the spatial rssr mechanism of the. A spatial kinematicchain may have cylindrical, spherical and helicaljoints. Kinematics analysis and optimization of carbonfree.
A classification scheme for planar 4r, spherical 4r, and. Spatial linkages are used to obtain mechanical inputoutput relationship between spatially oriented axes of movement. In order to verify the applicability of the synthesis methods presented in the thesis, the general loop closure equations of rshr. Wang wenbodepartment of industrial design and automation,beijing institute of clothing technology,beijing 29. Analytical and computeraided method for kinematics of.
In addition, system has an unbalance mass on disk 2. A mechanical linkage is an assembly of bodies connected to manage forces and movement. Sometimes, an ingenious arrangement will be able to simplfy a complex mechanism and accomplish the desired motion. Cognates and spherical hinge replacement of spatial rssr. The rssr spatial mechanism is the spatial analogy of the planar fourbar linkage. The material in this dissertation can be effectively divided into two subtopics. Our implementation of the rssr function generator inverts the linkage to transform the angular information into positions of the coupler of an rrss linkage. The connections between links are modeled as providing ideal movement, pure rotation or sliding for example, and are called joints. In order to design geometric parameters of spatial rssr mechanism in a shortcut effectively, based on motion character analysis of a particular spatial rssr mechanism, a combined method with 3d motion simulating and graphics parsing is introduced. Introduction, topology arrangements of robotics arms, kinematic analysis of spatial rssr mechanism, denavit hartenberg parameters, forward and inverse kinematics of robotic manipulators. Partially compliant spatial slidercrank rssp mechanism. A fourbar linkage, also called a fourbar, is the simplest movable closedchain linkage. The rssrss linkage is one of the most basic spatial multiloop.
A novel analysis and design approach of the compliant rssr mechanism with small length flexural pivots was presented by using its prbm. Yi zhang with susan finger stephannie behrens table of contents. A general spatial multiloop linkage optimization model. Dynamic analysis of a selected spatial onedof linkage mechanism with friction in joints characterized mechanisms, in fact being a family of the spatial linkage mechanisms, contain neither redundant dof nor passive constraints. Synthesis of an rssrss mechanism using a continuation method thiagaraj subbian and donald r. This paper resolves spatial rssr mechanism in dh coordinates to obtain its position equations.
The double crank rssr mechanism with constant transmission. A kinematic synthesizing method of spatial rssr transmission mechanismj. Evaluation of motiontransmission characteristics of rssr. Analytical and computeraided method for kinematics of spatial rssr mechanism haigang sun1, yong zhou2 1,2school of mechanical engineering, beijing institute of technology, beijing, china 1.
The dimensional conditions for the existence of spatial rssr mechanisms having constant transmission angle are investigated. However, mech designer is limited to those kinematicchains with sphericaljoint. Hence, it is also referred to as the skew fourbar linkage 3,4. Kemal ozgoren january 2005 the major part of this thesis has been devoted to path and motion generation synthesis of spatial. Dynamics of rigid flexible spatial four bar mechanism. Aiming at the computing complexity and complicated calculation procedures of kinematics analysis by mathematical methods, a formula on. The method of solution involves the selective precision synthesis technique to formulate the equality and inequality constraints which are then solved by the generalized reduced gradient method of optimization. Kinetic analysis of spatial rssr mechanism by analytical. Pdf this paper deals with the synthesis of the rssr mechanism, which is a spatial linkage with two revolute r and two spherical s kinematic pairs. Pdf on displacement analysis of the rssrss mechanism. The movement of a body, or link, is studied using geometry so the link is considered to be rigid. This course is basically concerned with the dualnumber coordinatetransformation matrix modeling of spatial mechanisms such as shaft couplings, spatial fourbars, spatial slider cranks. A rssp slidercrank mechanism has a revolute joint between the crank and the fixed link, two spherical joints connecting the crank and the slider to the coupler link, and a prismatic joint of arbitrary orientation.
Fung 69 and lin 1011 utilized different control approaches to investigate the response of. Beale 5 employed galerkins method to investigate the dynamic and stability of a flexible link used in a quick return mechanism. Request pdf a new type of compliant spatial fourbar rssr mechanism this paper presents a novel study on the analysis and design of a new type compliant spatial fourbar rssr mechanism. The dynamics of rigidflexible spatial fourbar mechanism was formulated for the following cases. The spatial rssr mechanisms with constant transmission angle. A threedimensional modeling, mathematical model analysis and solution function image combination method was proposed to design and analyze the rssr space fourbar transmission mechanism in this accessory, and the key parameters such as length and rotation angle was optimized. By extending robertschebyschev theorem, it is demonstrated mathematically that rssr mechanism possesses the same character as planer fourbar linkages in generating cognates. With the mathematical modeling,the spatial rssr mechanism kinematical example was analyzed based on the method of direction cosine matrix using matlab. With further motion simulation analysis, validity of the obtained parameters of rssr mechanism is verified. For most planar mechanism analysis, these standard classification methods are ideal.
This paper presents the synthesis of the rssrss path generating spatial mechanisms. Aiming at the computing complexity and complicated calculation procedures of kinematics analysis by mathematical methods, a formula on the relationship. This article presents a method for performing rssrss mechanism displacement analysis. Rssr mechanisms have oscillatory motions of the cranks and nonlinear relations are obtained between the input and output when compared to bevel gears. Drive optimization in the past, a single wheel drive scheme was used to realize the differential motion of the left and right wheels. Couplerbased synthesis of a rssr mechanism citeseerx. Although many methods are known for the kinematic analysis of spatial mechanisms, such as descriptive geometry, vector analysis, dual number theory. Optimized design of an rssr mechanism for an unpowered. The working stability of the spatial rssr mechanism effects directly working speed and binding quality of the binding line. They present a detailed kinematic analysis of the rrssr device with regard to steering linkage design and performance. Rssr mechanisms operate in a way similar to gear couplings with a more slender arrangement. The analysis of rssr spatial fourbar mechanism scholars mine. Synthesis and design of the rssr spatial mechanism for function generation. By utilizing the passive degree of freedom of the coupler of the rssr mechanism and its design equations sandor, g.
Spatial mechanisms with an introduction to robotics. Proofs of the grashof criterion can be found in williams and reinholtz 1986, paul 1979, and the extension to spatial rssr fourbar linkages in kazerounian and solecki 1993. Optimal counterweight balancing of spatial mechanisms. The proposed mechanism is a compliant version of rssr fourbar which is one of the most capable spatial mechanisms. Kinematic synthesis, spatial mechanism, algebra of. Spatial rssr mechanism design by graphics method based on 3d motion. In addition, they allow nonlinear relations with relatively large distances between axes. Synthesis of the optimal rssr mechanism for the motion.
Study and use of mechanism using simulation software packages. Thus, the transmission functions for each type of spatial mechanism can be easily obtained from the transmission function deduced in the general case of the rssr spatial mechanism 1, 2, 6. Kinematic analysis of threelink spatial mechanisms containing sphereplane and spheregroove pairs g. A cad addin for synthesis of rssr function generators. Angle and positions of maximal pressure angle of the spatial rssr linkage. Spatial rssr mechanism design by graphics method based on. Surprisingly, this 2dof fourbar spatial linkage has received little attention in the literature except for cursory descriptions. The first subtopic, philosophy of optimal mechanism design, is intended to be general in nature, applying to all types of mechanisms, both higher and lower pair, and both.
This paper deals with the synthesis of the rssr mechanism, which is a spatial linkage with two revolute r and two spherical s kinematic pairs, typically used to transmit rotational motion between shafts with skew axes. In this case, the dynamic analysis was done considering all three links i. So there is a future scope on working with rssr spatial mechanism. The creation of modern machines that can replace the work of people or perform movements of great complexity implies the need for the widespread use of spatial mechanisms. The rssr mechanism prototype was produced and demonstrated. A new type of compliant spatial fourbar rssr mechanism. A fully parameterized system model is established by using the differential method to calculate the running equation of the wheel. Dimensional synthesis, optimal transmissibility, rssr mechanism. The revolutesphericalsphericalrevolute or rssr mechanisms are simple. If we take the general case of the rssr spatial mechanism fig. J gilmartin work on rssr spatial mechanism early in the 1978.
A rssr spatial fourbar mechanism has two revolute joints of arbitrary orientation attached to the fixed link and two spherical joints connecting the cranks to the coupler link. Schematic diagram of the considered double fourbar crankslider mechanism 10 figure 2. Synthesis of multiloop spatial mechanisms by iterative. In a planar mechanisms, all of the relative motions of the rigid bodies are in one plane or in parallel. Compile a table of 1 dof spatial mechanisms having 2, 3 and 4 links let 4 5 0 j j in equation 3. With packaging, textile and automation machinery, the. However, all of their solutions are obtained numerically, rather than analytically. Considering strict requirements of spherical hinges in manufacture and assembly, this paper then addresses substitution.
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