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