Spatial Slider-crank Mechanism Research Articles

Design and analysis of a microminiature omnidirectional wave energy-harvesting device based on a spatial slider–crank mechanism

Energy-harvesting devices using wave energy and ocean current energy can provide higher endurance and operation capacity for small floating or mobile equipment in offshore operations. In this paper, a microminiature omnidirectional wave energy-harvesting device based on a spatial slider–crank mechanism was designed for equipment whose length is less than ordinary ocean wavelength. It can harvest the ocean wave energy from the omnidirectional swing of the buoy and convert the reciprocating swing motion of the buoy into the unidirectional rotation motion of the generator to improve the energy conversion efficiency. The dynamic model and equivalent circuit model of the energy-harvesting device were established by the Lagrangian method and circuit-based analysis method, respectively. The model was simulated, and the effects of parameters such as crank length, wave period, etc. were investigated. The results showed that the device has good energy-harvesting performances, especially in medium and low sea conditions. In addition, the performance of the device can be improved by adjusting the length of the crank and rod.

Local-Coordinate Representation for Spatial Revolute Clearance Joints Based on a Vector-Form Particle-Element Method

Previously, the contact states between the bearing and journal of a spatial revolute joint (SRJ) with both axial and radial clearances were solved in the global coordinate system (GCS), which is complex and requires iterations. In this paper, a local-coordinate representation for the SRJs with clearance is combined with a vector-form particle-element method, i.e. finite particle method (FPM), to provide a more practical means for evaluation of the dynamic effects due to clearance. Firstly, the fundamentals of the FPM for analysis of spatial mechanisms are briefed. Then, a local-coordinate representation based on the revolution axis of the bearing is proposed. Specifically, the geometry of the journal and bearing is explicitly expressed using the coordinate transformation. The axial and radial contact states are evaluated by substituting the parametric equations and transforming them to quadratic and quartic equations, respectively, which can be analytically solved without iterations. The contact forces are evaluated in the local-coordinate representation and then transformed into the GCS representation. Two numerical examples, i.e. a spatial slider-crank mechanism and a spatial double pendulum, are provided to demonstrate the feasibility of the proposed method, by which the effects of joint-joint interaction and joint-flexible component interaction are fully discussed.

Augmented Lagrangian index-3 semi-recursive formulations with projections

MBSLIM (Multibody Systems at Laboratorio de Ingenieria Mecanica) multibody library includes some global formulations for the dynamics and sensitivity analysis of multibody systems. The extension of the library to accommodate topological formulations in relative (joint) coordinates and their implementation are going to be described in two separate works, this one being devoted to dynamics and the second one to a sensitivity analysis. With this extension in the scope, some topological semi-recursive formulations derived in the past are revisited, generalized and reformulated. The need for generalization of the previously published formulations was detected because the equations proposed were not general enough to be integrated in an all-purpose multibody library in natural coordinates like MBSLIM, especially because both set of coordinates need to coexist, the definition of the mechanisms has to be the original one and the library has to be automatic and all the existing models have to work with the new approach. Moreover the new solver takes advantage of some problems solved in natural coordinates, like the initial position and initial velocity problems for closed-loop systems. Finally, to test the new equations, two benchmark problems are presented and their results compared: a spatial slider–crank mechanism and a buggy vehicle model.

Analysis of the joint clearance effects on a compliant spatial mechanism

This study investigates the dynamics of a partly compliant mechanism with joint clearance. A spatial slider–crank mechanism is used as a numerical example. The kinematic and dynamic performances of articulated and compliant mechanisms are compared to each other. As a pseudo joint, a multi-axis small-length flexural pivot is used to ensure the necessary mobility between the connecting rod and piston links. In order to simplify the analysis, pseudo-rigid-body model is transferred to the analytic equations of compliant mechanism. The results show that clearance in joints leads to chaotic behaviour on the kinematic and dynamic outputs of the mechanisms. Due to the flexibility effect of small pivot and the relation of force-closed kinematic pair between the ball and socket in a clearance joint, compliant mechanism offers a good solution to decrease the chaotic phenomenon arising from clearance in mechanism's outputs. Also, for minimizing the partly resistive behaviour of pseudo joint relative to the mechanism motion, material and geometric features of small flexural pivot can be used as design variables.

Single piece compliant spatial slider–crank mechanism

This paper presents a novel study on the analysis of the “single piece” compliant spatial slider–crank mechanism. In the previous study performed by the authors, a “partially compliant” version of the spatial slider–crank mechanism was introduced. Since there was a rigid ball joint in that case, there was no torsional loading at flexural hinges. For the single piece case, there is no ball joint in the structure of the mechanism. Therefore, there is also torsion available at multiple axis flexural hinges. Analysis and design of such a compliant mechanism is different from the partially compliant case. In this study, deflections of the multiple axis flexural hinges are determined as bending and twist separately. Fundamental angles for manufacturing a mechanism in a particular position are obtained. A real model is built and results of the mathematical model are verified with experiments. A fatigue test is performed for flexural hinges of a similar mechanism. After one and a half million cycles it is monitored that there is no indication of failure.

Spatial compliant constant-force mechanism

In this study, a novel constant-force mechanism (CFM) is introduced. A design method is proposed to employ the compliant spatial slider-crank mechanism as CFM. Design geometry and initial conditions are presented for the selected configurations of the compliant constant-force mechanism (CCFM). Design parameters are nondimensionalized. Parameters of the PRBM that result in a CFM are determined via minimizing the variation in the output force over the given input displacement. A generalized solution method is derived to determine optimum results and some design charts are presented. In order to verify feasibility of the design procedure, a real model is built and it is shown that the experimental results are consistent with the theoretical approach.

Real-time flexible multibody simulation with Global Modal Parameterization

Many applications require fast and even real-time multibody simulations. Until recently, strongly simplified models were used in order to reach real-time constraints. A novel system-level model reduction technique, namely Global Modal Parameterization (GMP), enables the reduction of a complex mechanism, incorporating flexibility. This technique groups all computationally demanding tasks in a preprocessing phase, which allows the actual simulation to run at real-time. The main strength of the algorithm lies in the fact that the original system of differential-algebraic equations is transformed into a system of ordinary differential equations, which can easily be integrated with explicit methods. This work shortly reviews the GMP-method for systems undergoing 3D motion with multiple rigid DOFs. Furthermore the framework for hard real-time simulation with GMP is discussed. The novelty is the description of a simulation method for a GMP model with an explicit time integrator, which is deployable on hard real-time systems. One of the method’s advantages is the a priori known computational load for each timestep, allowing hard real-time simulations. The method is benchmarked for a flexible spatial slider-crank mechanism, modeled in a commercial flexible multibody package. This is the first application of the GMP-approach on an original floating-frame-of-reference component mode synthesis model undergoing highly dynamical motion.

Parameter Identification in Multibody Systems Using Lie Series Solutions and Symbolic Computation

This paper studies the application of the Lie series to the problem of parameter identification in multibody systems. Symbolic computing is used to generate the equations of motion and the associated Lie series solutions automatically. The symbolic Lie series solutions are used to define a procedure for computing the sum of the squared Euclidean distances between the true generalized coordinates and those obtained from a simulation using approximate system parameters. This procedure is then used as an objective function in a numerical optimization routine to estimate the unknown parameters in a multibody system. The effectiveness of this technique is demonstrated by estimating the parameters of a structural system, a spatial slider-crank mechanism, and an eight-degree- of-freedom vehicle model.

Modeling 3D revolute joint with clearance and contact stiffness

The clearances in the kinematic joints are due to deformations, wear, and manufacturing errors; the accurate modeling of these effects in multibody analysis is a complex issue but in many practical applications, it is mandatory to take into them into account in order to understand the actual behavior of mechanical systems. In this paper, the authors present a general computer-aided model of a 3D revolute joint with clearance suitable for implementation in multibody dynamic solvers. While a perfect revolute joint imposes kinematic constraints, the proposed revolute joint with clearance leads to a force constraint. The revolute joint has been modeled by introducing a nonlinear equivalent force system, which takes into account the contact elastic deformations. The model depends on the structural and geometrical properties of materials in contact that have been investigated using finite element models. The purpose is to give a general approach to study the influence of actual joints on kinematic, dynamic, and structural behavior of mechanisms. The proposed model has been applied in dynamic simulations of a spatial slider-crank mechanism.

Comparison between mathematical modeling and experimental identification of a spatial slider–crank mechanism

In this paper, Hamilton’s principle, Lagrange multiplier, geometric constraints, partitioning method and Baumgarte stabilization method (BSM) are employed to derive the dynamic equations of a spatial slider–crank mechanism that is driven by a servomotor. The formulation considers the effects of links masses, external forces and motor electric inputs. Comparing dynamic responses between the experimental results and numerical simulations, dynamic modeling gives a wonderful interpretation for the spatial slider–crank mechanism. In this paper, a new identification method based on real-coded genetic algorithm (RGA) is presented to identify the parameters of a spatial slider–crank mechanism. The method promotes the calculation efficiency very much, and is calculated by real-code without the operations of encoding and decoding. The results of numerical simulations and experimental results prove that the identification method is feasible. The contributions of this paper are that the comparison of mathematical modeling and identification between numerical simulations and experimental results are all realized.

The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367–391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy–momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method.

Balancing conditions of spatial mechanisms

The article proposes a method to algebraically derive the balancing conditions for shaking force and shaking moment of spatial one-degree-of freedom mechanisms. These include formulae for complete elimination of the shaking force and the shaking moment caused by all moving links. The method has advantage of being suitable for the application of the widely accessible computer algebra systems such as MAPLE ® . In the example, the algebraic balancing conditions for shaking force and shaking moment of a spatial slider crank mechanism are given.

Kinematic and Kinetic Derivatives in Multibody System Analysis*

Analytical formulas for kinematic and kinetic derivatives needed in multibody system analyses are derived. A broad spectrum of problems, including implicit numerical integration, dynamic sensitivity analysis, and kinematic workspace analysis, require evaluation of first derivatives of generalized inertia and force expressions and at least three derivatives of algebraic constraint functions. In the setting of a formulation based on Cartesian generalized coordinates with Euler parameters for orientation, basic identities are developed that enable practical and efficient computation of all derivatives required for a large number of multibody mechanical system analyses. The formulation is verified through application to a spatial slider crank mechanism and a 14 body vehicle model. Efficiency of computation using the expressions derived is compared with results obtained employing finite differences, showing significant computational advantage using the analytically derived expressions.

On the shaft locations of two contra-rotating counterweights for balancing spatial mechanisms

It has been shown in a previous work that a frequency term of the shaking force of spatial mechanisms, whose hodograph is proved to be an ellipse, can be eliminated by a pair of contrarotating counterweights. In this work, it is found that the relevant frequency term of the shaking moment is minimized if the balancing shafts are coaxial at the centre of a family of ellipsoids, called isomomental ellipsoids, with respect to (w.r.t.) any point on an ellipsoid, as is also the root mean square (r.m.s.) of the relevant frequency term of the shaking moment. It can also be minimized even though the location of either shaft, but not both, is chosen arbitrarily on a plane. The location of the second shaft is then determinate. In order to locate the centre, a derivation for the theory of isomomental ellipsoids of a frequency term of the shaking moment of spatial mechanisms is given. It is shown that the r.m.s. of a frequency term shaking moment of a spatial mechanism w.r.t. the concentric centre of the isomomental ellipsoids is the minimum. Examples of a seven-link 7-R spatial linkage and a spatial slider-crank mechanism are included.

A finite element dynamic analysis of spatial mechanisms with flexible links

A finite element based method is presented for dynamic analysis of spatial mechanisms with flexible links. In this analysis the geometrically nonlinear relations for the element deformations in terms of the nodal position and orientation coordinates play a central role. The equations of motion are formulated in terms of mixed sets of generalized coordinates of the mechanism with rigid links and deformation mode coordinates that characterize deformation of the elements. A dynamic simulation of a spatial slider crank mechanism with flexible connecting rod and a simulation of a rotating shaft passing through the major critical speed is presented.

Selective Precision Synthesis of the Spatial Slider Crank Mechanism for Path and Function Generation

A technique for the synthesis of the RRSC spatial slider crank mechanism for path and function generation using the Selective Precision Synthesis method is presented here. Also presented is a closed form analysis technique for this mechanism. The analysis uses the spatial rotation matrices to obtain a fourth order polynomial for the coupler link rotations with the coefficients expressed in terms of the link lengths and input link rotation. This polynomial is solved in closed form to determine the coupler link rotations which are then used to determine the locations of the path point, the output link rotations, and the displacement of the slider at the cylindrical joint. For synthesis, nonlinear inequality constraint equations relating the generated and the desired path points (or slider displacements) are formulated. These constraints define accuracy neighborhoods around each of the “n” prescribed path points (or slider displacements), and are solved using the Generalized Reduced Gradient method of optimization.

The design of an adjustable, three dimensional slider crank mechanism

This paper presents a technique for the design of an adjustable spatial slider crank mechanism to be used as a variable displacement pump or compressor. The design method considers velocity fluctuation, force transmission effectiveness and mechanism geometric proportions. An example application is provided.

An Improved Alternative to the Three-Dimensional, Swash Plate Mechanism

This paper presents a theoretical analysis and a design technique for the use of a special type of adjustable spatial slider crank mechanism to replace the swash plate device commonly used as a variable displacement pump or compressor. This paper is an extension of a previous research effort utilizing the RSSP mechanism [7] and considers the influence of geometric proportions of a device on stroke size, velocity fluctuation, and force transmission effectiveness. The device is shown to have significant kinematic advantages over the traditional form of the swash plate mechanism. Design curves are presented and an example application is provided.

Synthesis of optimum slider-crank mechanisms

For the spatial slider-crank mechanism formulas are obtained to allow the user determine the link sizes and slider offset for a predetermined stroke with an acceptable pressure angle at the extremes of slider travel as well as by a given angle between the crosshead guide of the slider and a plane in which the crank revolves. Formulas for determining the sizes of links of the plane slider-crank mechanism as a special case of the spatial mechanism are also presented. The particular cases of mechanisms havingequal angles of pressure as well as at extreme values of an angle between crosshead guide and the revolution plane of the crank are discussed. It is shown, that the plane mechanism case provides maximum slider travel when other things are equal.

Synthesis of spatial slider-crank mechanism for given slider stroke and crank length

With the end positions of the stroke and the radius of the crank specified, the locus of the fixed end of the crank in the plane of crank rotation can be graphically or analytically determined.