RSSR Mechanism Research Articles

Design and parameter optimization of solid-surface antenna parallel mechanism constructed by multi-loop spatial coupling units

The optimization of design and structural parameters of solid-surface antennas is crucial for the development of aerospace satellites. In this paper, the study explores an innovative parallel solid-surface antenna mechanism, inspired by the daisy bloom pattern, which realizes the characteristics of Fewer input-More output (Fi-Mo). A single-DOF deployable/foldable spatial multi-loop coupled mechanism model of the bionic daisy solid-surface antenna is established based on the single-axis tilting hinge, RSSR mechanism, and Bennett mechanism. The motion characteristics of the antenna mechanism are analyzed using the topology, position and orientation characteristic (POC) and inverse screw theory. The error transfer law of multi-loop mechanism is derived by the low-layer-loop sequence. The optimal configuration parameter set of the antenna deployment mechanism is determined using the NSGA-II genetic algorithm. Finally, the optimized antenna mechanism is subjected to physical simulation analysis to verify its stability and the accuracy of its deployment path.

RSSR Mechanism Design and Motion Control Strategy of a Carbon-Free Vehicle for Obstacle Avoidance Competition

RSSR Mechanism Design and Motion Control Strategy of a Carbon-Free Vehicle for Obstacle Avoidance Competition

On spatial relations to the Euler-Savary formula

The Euler-Savary formula is a well-established relation with multiple interpretations. This formula is revisited and cast as a geared three-link spatial mechanism with uniform motion and gear rotation axes without axial pitch. Two versions of the spatial Euler-Savary formula emerge; the classical version that matches motion parallel to the ISA and a new version that matches motion perpendicular to the ISA akin to the planar scenario. These two versions are combined resulting in a circle line surface of moving axes together with a conjugate center line surface of stationary axes. These two surfaces define axis pairs used to match second-order axode motion. Also included are inflection surfaces as the spatial analog to the planar inflection circle. One of the inflection surfaces is contrasted with an invariant relative curvature surface. Subsequently, a ruled surface is presented to emulate the planar Bresse circle by combining two axes on the inflection surface to establish a third axis on a Bressesque surface. Lastly, an RSSR mechanism is presented by combining aspects of the invariant curvature surface and an R-R interpretation of the Euler-Savary formula.

Biomimetic Robotic Sea Lion Foreflippers: Design, Modeling, and Experimentation

Otariidae are excellent swimmers and the only ones among the marine mammals that use foreflippers for propulsion. Taking California sea lion as the bionic prototype, this article proposed and developed a biomimetic robotic sea lion foreflipper device (robotic flipper for short), which is composed of a pair of bionic flippers and a serial mechanism consisting of a wobbling coin mechanism and a RSSR spatial crank-rocker mechanism. The attitude and motion characteristics of the bionic flipper were obtained based on the kinematic analysis of the robotic flipper. Kinematic analysis and tank experiments show that the robotic flipper can effectively imitate the motion characteristics of the sea lion foreflipper. In addition, it can also obtain different flipper tip trajectories by adjusting the length of the connecting rod of the RSSR mechanism, and the generated thrust from the trajectory like sea lion foreflipper is larger than that from other flipper tip trajectories. A higher clapping frequency can generate a higher thrust, and the bionic flexible flipper has higher thrust and thrust efficiency than the rigid one. A larger pitch angle of the robotic flipper can result in a larger peak thrust but not always a larger average thrust. The present robotic flipper shows a better thrust performance at the pitch angle of 15°.

Investigation of spatial plane joint characteristic for dynamic analysis of VSV mechanism based on similarity scaling technique

The Variable Stator Vane (VSV) mechanism is utilized to adjust the stator vane angles so as to delay the compressor stall. Establishing the dynamic model of the system, which is the basis to obtain different joint characteristics more in line with the real case, is worth analyzing. In this work, a comprehensive dynamic model of the scaled system of VSV mechanism’s single kinematic chain by the Lagrange multiplier method is built, thus the spatial plane joint characteristic’s effects on the behavior of the scaled system are investigated. Since a full-scale facility is unavailable for testing sometimes, the technique of similarity scaling is resorted to establishing the scaled principle-level model which has a certain relationship with the prototype in structure and material and so on. Then an example of the dynamic modeling procedure of the spatial RSSR mechanism included in the scaled model is presented with the aim of establishing a guide to model the whole system. Therefore, the equation of motion of the scale system is expediently established using some systematic method. Finally, inertial navigation sensors are used to measure the corresponding displacement for evaluation with accuracy of the established dynamic model.

Dynamic investigation of a spatial multi-body mechanism considering joint clearance and friction based on coordinate partitioning method

The dynamic response of the model, which is the series connection of a planar four-bar mechanism and a spatial RSSR mechanism, is analyzed considering revolute joint clearance and friction. A non-holonomic constraint equation is proposed to solve the Euler angles. The dynamic equations are established by combining the Lagrange equation with the modified contact model and the LuGre friction model. A dynamic solution program based on the coordinate partitioning method is designed to solve the dynamic equations. The paper verifies the correctness and applicability of the solution program by comparing the numerical calculation results with Adams simulation. Compared with the results of eccentricity, it is found that the maximum penetration is very sensitive to the change of the slider speed rather than the clearance. The equivalent damping coefficient proposed by authors not only represents whether a collision occurs, but reflects the hysteresis caused by damping. The macroscopic manifestation of the up and down oscillation of eccentricity is the swing of the contact point. Besides, the system quickly changes from the collision into the stable state due to considering friction, and the peak value of each collision reduces greatly. Therefore, when the clearance is unavoidable, the clearance joint should be coated with a material with a large friction coefficient and not easy to wear.

Parameter Optimization and Experiment of Soil Cleaning Device on Apple Seedling-Lifting Machine Based on Spatial RSSR Mechanism

HighlightsThe spatial four-bar linkage mechanism is applied to the apple orchard seedling-lifting machines.The dimension synthesis of spatial four-bar mechanism is applied to the design of agricultural machinery.A new type of soil cleaning device for apple orchard seedling-lifting machines was designed.Compared with the traditional soil cleaning device, the new soil cleaning device with optimized parameters causes less damage to root system and provides a more stable performance.Abstract. To solve the problems of poor working conditions, incomplete root systems, and low seedling-lifting efficiencies of apple orchard seedling-lifting machines, a new type of shaking soil-cleaning device was proposed, in which a spatial four-bar linkage (RSSR) was used instead of a traditional planar linkage. By means of the direction cosine matrix, the position and pose of the spatial four-bar mechanism of the device were analyzed, and the functional relationship was obtained. A fast Fourier transform (FFT) was used to synthesize a periodic function of the spatial four-bar linkage, a numerical atlas was established, and the dimensions were selected by means of fuzzy recognition. A genetic algorithm (GA) was used to optimize the identified parameters, and the optimized mechanisms was compared with the traditional planar linkage mechanism. The results showed that the maximum positive and negative errors of the first curve fitting groups were 0.43% and 0.67%, respectively, and those of the second curve fitting group were 0.79% and 0.50%, respectively, which met the operating and precision requirements. The structure of the new oscillating soil cleaning device is compact. Meanwhile, moderate lengths of the main roots, dense root hair, and complete root systems were achieved. The results showed that the taproots remained intact, and they were between 120 and 150 mm long. Due to the small sample size, the damage rate of the seedlings was zero, and the seedlings produced by the two models met the agronomic requirements. Thus, the requirements of agricultural operations are met by the optimized mechanism. This design concept can provide ideas for follow-up spatial RSSR four-bar mechanism design, and the optimized size parameters can provide a reference for the follow-up design and research of seedling and soil clearing devices. Keywords: Dimension synthesis, Genetic algorithm, Numerical atlas method, Oscillating soil cleaning device, Spatial RSSR mechanism.

Kinematics Analysis and Optimization of Carbon-Free Vehicle of "8"-Shaped Trajectory Based on Spatial RSSR Mechanism

In view of the low stability of the carbon-free 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. A fully parameterized system model is established by using the differential method to calculate the running equation of the wheel. The whole optimization method is obtained by using the calculation function of MATLAB to simulate the motion of the system, and the trajectory of the car is optimized.

Dimensional synthesis of the optimal RSSR mechanism for a set of variable design parameters

This paper deals with the dimensional synthesis of the RSSR mechanism, also known as spatial four-bar linkage (R and S stand for revolute and spherical kinematic pairs respectively). To univocally describe the geometry of the RSSR mechanism a specific set of geometry parameters is necessary. Generally speaking, in a synthesis problem a subset of these parameters, defined as design parameters, is usually considered as assigned whereas the remaining ones, defined as design variables, have to be found by the synthesis procedure. That is, the goal of the synthesis procedure is to find the values of the design variables, while satisfying both functional requirements of the mechanism and constraints on the design parameters. In this paper each design parameter is assigned as variable within a given range rather than being assigned as a single value. In general, varying a design parameter means obtaining a different mechanism which has different functional performances as a consequence. This feature gives raise to a novel synthesis problem, which has not been treated in the literature yet. In particular, the RSSR mechanism synthesis presented in this paper takes the optimization of the force transmission as an objective function, while referring to a given range of values of each design parameter. In addition, prescribed constraints on given extreme angular positions for both the input and the output links, on the upper and lower bounds for the transmission ratio, and on the upper and lower bounds for the design variable values have to be satisfied. The synthesis problem, set as a constrained minimization problem, is solved numerically in two steps by means of a Genetic algorithm followed by a quasi-Newton algorithm. As an example of application, a dimensional synthesis of an RSSR mechanism used in a hand exoskeleton is reported.

Kinetic Analysis of Spatial RSSR Mechanism by Analytical Method

Aiming at the complexity of kinetic analysis of spatial mechanism by analytical method, an analysis model is established in 3D Cartesian coordinate system. 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. Through computer-aided tools, the corresponding curves are plotted, even the correctness of analytical method is validated. In virtual prototype environment, the same analytical results are presented, giving above conclusions a convincing support. This dissertation actualizes the effective kinetic analysis of spatial RSSR mechanism and has valuable reference to the parametric analysis and design.

Cognates and Spherical Hinge Replacement of Spatial RSSR Mechanism

This paper resolves spatial RSSR mechanism in D-H coordinates to obtain its position equations. By extending Roberts-Chebyschev Theorem, it is demonstrated mathematically that RSSR mechanism possesses the same character as planer four-bar linkages in generating cognates. Considering strict requirements of spherical hinges in manufacture and assembly, this paper then addresses substitution methods of spherical hinge in RSSR mechanism, including constraining DOF of spherical pair by specific structural dimensions and replacing high pair by combinations of low pairs, while taking examples of sphere 4R mechanism, spatial orthogonal crank-rocker mechanism and spatial 6R mechanism in dobby machine. Physical kinematic simulation is done in the environment of MSC.ADAMS to validate the feasibility of spherical hinge replacement, providing guidance and reference to future design of complex spatial mechanisms.

A New Approach to Dimension Synthesis of Spatial Four-Bar Linkage Through Numerical Atlas Method

This paper presents a new method for the synthesis of spatial mechanism. Using harmonic analysis, the coupler curve and output angle function of spatial mechanism can be described as a series of harmonic characteristic component. For the path generation problem of the spatial mechanism, a technique of normalization processing eliminates the effects of scale, translation, and rotation; in other words, the harmonic characteristic component of the coupler curve is just determined by the basic dimensional type of spatial mechanism but not by the real dimension and the installing position. The numerical atlas database of coupler curve or output angle function of spatial mechanism can be created by the harmonic characteristic components and associated basic dimensional type of spatial mechanism. The best suitable basic dimensional type of spatial mechanism for prescribed function can be decided by using fuzzy identification method and numerical atlas database. On the basis of the basic dimensional type and formulas, which compute the coupler point, true size, and installing dimensions of the spatial mechanism, the dimension synthesis of the spatial mechanism is made possible. This paper takes the RSSR mechanism and RRSS mechanism as an example to illustrate the analysis process and application of this method.

Transformation from Spatial RSSR Mechanism to Spherical 4R Mechanism

A method of transformation from spatial RSSR mechanism to spherical 4R mechanism for spatial driving mechanism design is presented. The necessary conditions of transformation from spatial RSSR mechanism to spherical 4R mechanism are also analyzed. Furthermore,it is proved theoretically that,spatial RSSR mechanism,by defined parameters,can be transformed into spherical 4R mechanism with axes intersection at one point. The prerequisite for each design parameter in transformation from spatial RSSR mechanism to spherical 4R mechanism,when spatial RSSR acts as a driving crank,is thus deduced,which lays a theoretical basis for the application of practical engineering. Based on the method of transformation from spatial RSSR mechanism to spherical 4R mechanism,theoretical calculation and test simulation,a spatial rapier-driving mechanism applicable for high-speed rapier looms is developed. Through this example,this method that spatial RSSR mechanism is replaced by spherical 4R mechanism is verified. The finding indicates that all the requirements of spatial RSSR mechanism can be met and the spherical 4R shows better performance,manufacturability and assemblability. Priority of spherical 4R mechanism is also validated in terms of structure,manufacturability,maintenance and kinematics and dynamics performance.

An optimization technique for the balancing of spatial mechanisms

This paper presents a new generic optimization technique for the balancing of the shaking force and shaking moment due to inertia forces in spatial mechanisms. For given dimensions and input speed of a mechanism, the inertia forces depend only upon the mass distribution of the moving links. The equimomental system of seven point-masses is introduced to represent the inertial properties of the links and to identify optimizing variables. The effectiveness of the proposed methodology is illustrated using a spatial RSSR mechanism.

Mobility Analysis of RSSR Mechanisms by Working Volume

An RSSR mechanism is analyzed by treating the linkage as two manipulators. The mobility region of the input link or the output link is derived from the intersection region of the working volumes generated by two manipulators. It can be found by solving the region bounded by an ellipse and a unit circle. Concise discriminants and straightforward strategy are developed to determine the type for some special RSSR linkages. Grashof’s rule is derived for determining the type of planar four-bar and proved to be the primary criterion for simply skewed four-bar.

On Realization of Spherical Joints In RSSR Mechanisms

A spherical joint must allow adequate mobility between the ball and socket. Unless the specific geometric requirement of the spherical joint, namely the trajectory of the ball stem in the socket, is known, the realization of a synthesized mechanism containing a spherical joint can become an endless trial and error process or even a fruitless attempt. Typical examples can be found in RSSR mechanisms. For a synthesized RSSR mechanism, this paper presents the closed form equation describing the spherical trajectory of the ball in the socket and the design and manufacturing issues of the spherical joints. It offers the classification scheme of spherical joints based on the required ball rotatability in the socket and shows how the necessary socket opening of the spherical joints is affected. The size and location of the socket in a spherical joint must be properly determined to meet the rotatability requirement and in many situations, a conventional spherical joint with a circular socket opening cannot be used. Essential geometric and location information regarding to the use of non-circular socket opening, spherical grooved pair, as well as revolute joints to replace the conventional spherical joints to realize a synthesized RSSR mechanism is presented. The proposed concept and method can be extrapolated to other mechanisms containing spherical joints.

空間RSSR機構の動力学的最適設計におけるリンク形状の最適化(S46-1 機構の開発とシミュレーション(I),S46 機構の開発とシミュレーション)

空間RSSR機構の動力学的最適設計におけるリンク形状の最適化(S46-1 機構の開発とシミュレーション(I),S46 機構の開発とシミュレーション)

Mobility analysis of RSSR linkage and type maps of special cases

An RSSR mechanism is analyzed by treating the linkage as two manipulators. The intersection region of the working volumes generated by both manipulators represents the mobility region of the input link or the output link. Finding the mobility region is to solve equations of an ellipse and a unit circle mathematically. For planar four-bar, one of the special RSSR linkage, Grashof’s rule is derived. The method of efficiently determining the type of a simply skewed four-bar is also proposed. For the purpose of synthesis, the type maps for planar and simply skewed four-bar are performed. The abscissa and ordinate of the map are the lengths of input link and output link, respectively. With developed type maps, the lengths of both input and output links can be selected easily when synthesizing a linkage with specified type.

On Displacement Analysis of the RSSR-SS Mechanism

This article presents a method for performing (RSSR-SS) mechanism displacement analysis. The benefit of this method is that it provides a practical alternative for performing RSSR-SS mechanism displacement analysis and is fully applicable with today's mathematics software. This method is an extension of the adjustable RSSR-SS synthesis method developed by the authors (Suh, C. H., Radcliffe, C. W. (1978). Kinematic analysis of spatial mechanisms. In: Kinematics and Mechanism Design. New York: John Wiley and Sons, pp. 179–183). By utilizing the passive degree of freedom of the coupler of the RSSR mechanism and its design equations (Sandor, G. N., Erdman, A. G. (1984). Spatial mechanisms with an introduction to robotics. In: Advanced Mechanism Design Analysis and Synthesis. Englewood Cliffs: Prentice-Hall, pp. 635–641), the design equation for the remaining (S-S) link of the RSSR-SS mechanism was developed using spatial transformation matrices under the constant length condition of the remaining S-S link. The angular rotation about the coupler of the RSSR mechanism, satisfying the constant length equation of this remaining S-S link, was calculated, numerically (Allen M. B. III, Isaacson, E. L. (1998). Solution of non-linear equations. In: Numerical Analysis for Applied Science. New York: John Wiley and Sons, pp. 177–187). As an example, the displacement of a series of rigid body points on the coupler of an adjustable RSSR-SS mechanism was calculated for a range of prescribed crank angles.

Optimum Balancing of Shaking Force and Shaking Moment for Spatial RSSR Mechanism Using Genetic Algorithm.

In this paper, we propose a new method, the comprehensive mass distribution method, for an optimum balancing of the shaking force and shaking moment of spatial RSSR mechanism (a spatial four-bar mechanism with two Revolute and two Spherical joints). The method consists of two parts:(1) optimizing the mass distribution of the link itself, and (2) adding weights to the end of the link. A genetic algorithm as an optimization technique is used in this study. Some examples are given, and the results show that the balancing effectiveness of the new method is better than that achieved by the conventional method and the weight of the mechanism is decreased. The shapes of optimized links are obtained using the small element superposing method.