Planar Mechanisms Research Articles

Multi-objective Dimensional Optimization of a 3-DOF Translational PKM Considering Transmission Properties

Multi-objective dimensional optimization of parallel kinematic manipulators (PKMs) remains a challenging and worthwhile research endeavor. This paper presents a straightforward and systematic methodology for implementing the structure optimization analysis of a 3-prismatic-universal-universal (PUU) PKM when simultaneously considering motion transmission, velocity transmission and acceleration transmission. Firstly, inspired by a planar four-bar linkage mechanism, the motion transmission index of the spatial parallel manipulator is based on transmission angle which is defined as the pressure angle amongst limbs. Then, the velocity transmission index and acceleration transmission index are derived through the corresponding kinematics model. The multi-objective dimensional optimization under specific constraints is carried out by the improved non-dominated sorting genetic algorithm (NSGA II), resulting in a set of Pareto optimal solutions. The final chosen solution shows that the manipulator with the optimized structure parameters can provide excellent motion, velocity and acceleration transmission properties.

A novel approach of input tolerance design for parallel mechanisms using the level set method

Input uncertainties inevitably result in the output error for parallel mechanisms, which will lead to significant influence on good work performance. To control the output error within the specification boundary, this article proposes a novel approach of input tolerance design based on the level set method for the driving joint. The implementation of the proposed method can be divided into two subtasks. First, using the level set method, the exact input error boundary is determined by means of evolving an initial input error interface with a defined normal speed field, thereby transforming the problem of exploring the exact boundary into solving a partial differential equation with initial value. On this basis, according to the equal and scaled principles, the tolerance width of each input is evaluated in an intuitionally geometrical manner, that is, searching the maximum geometry corresponding to the principle inside the exact input error boundary. Finally, two planar parallel mechanisms with different degrees of freedom are introduced as numerical examples to demonstrate the execution and effectiveness of the proposed method.

Non-probabilistic kinematic reliability analysis of planar mechanisms with non-uniform revolute clearance joints

Owing to the inevitable phenomena in which the wear of a revolute joint is non-uniform and severely affects the output motion accuracy, a conservative and efficient motion accuracy evaluation of mechanisms considering non-uniform wear is required by designers. Hence, this paper presents an integrated non-probabilistic kinematic analysis of precision mechanisms with non-uniform wear in joint by combining multi-body dynamic analysis, wear prediction and kinematic reliability analysis. The presented accuracy measurement and corresponding solution strategy can be used as the objective or constraint in dimensional synthesis to realise a longer service life. The non-uniform clearance is quantified by unknown but bounded variables, the boundary of which is expressed by the B-spline function. Furthermore, the kinematic reliability is calculated based on the non-probabilistic interval interference model. Two numerical examples consisting of wear prediction, motion error quantification, and reliability evaluation are presented to demonstrate the validity and applicability of the developed methodology.

Effects of passive vibration absorbers on the mechanisms having clearance joints

In the current study, the dynamic behavior of two planar mechanisms with revolute joints, in the presence of clearances is investigated. Subsequently, a control scheme with the aim of restraining the clearance and maintaining a more stable behavior is proposed. This approach is based on using tuned mass damper (TMD) in order to reduce the effects of clearances in mechanisms for passive control purpose. The applied absorber’s mass is insignificant and they are little in size. By attaching two perpendicular absorbers in order to control the clearance, the oscillations are notably reduced. The proposed methodology is applied to planar multibody mechanical systems with revolute clearance joints with a view to demonstrating its features. The absorber performance is evaluated for changes around the designed state and the results show that the designed absorbers have a good robustness with variations to changes in different parameters.

On a Two-DoF Parallel and Orthogonal Variable-Stiffness Actuator: An Innovative Kinematic Architecture

Variable-Stiffness Actuators are continuously increasing in importance due to their characteristics that can be beneficial in various applications. It is undisputed that several one-degree-of-freedom (DoF) solutions have been developed thus far. The aim of this work is to introduce an original two-DoF planar variable-stiffness mechanism, characterized by an orthogonal arrangement of the actuation units to favor the isotropy. This device combines the concepts forming the basis of a one-DoF agonist-antagonist variable-stiffness mechanism and the rigid planar parallel and orthogonal kinematic one. In this paper, the kinematics and the operation principles are set out in detail, together with the analysis of the mechanism stiffness.

Geometric Design With Multiple Realizable Motion Tasks in the Vicinity of a Planar Mechanism–Environment Contact

Abstract This paper applies geometric design principles to planar mechanical systems, attempting to explain complex motion in mechanism–object/environment interaction for realizing multiple kinematic tasks in the vicinity of a contact location. The latter is a critical feature not fully captured in existing design methodologies. This is achieved through the development of a general planar geometric model that allows the derivation of multiple velocity and acceleration specifications compatible with mechanism–object curvature constraints in the vicinity of the contact. By incorporating these higher-order kinematic specifications into the design task formulation, contemporary planar kinematic synthesis is generalized allowing robust designs. The results are illustrated by the kinematic synthesis of two planar revolute–revolute (RR) linkages that are able to push and roll-slide along the object’s curvature in the vicinity of a contact location, a hybrid hand that incorporates a four-bar prosthetic finger that is able to grasp objects in two different modes, and a six-bar orthotic wheelchair for disabled canines that integrates body tilt and climbing motions.

The optimum distance function method and its application to the synthesis of a gravity balanced hoist

The objective of this paper is to design and analyse a gravity balanced hoist composed of a cable drum, four-bar linkage and spring. A new mechanism synthesis problem is formulated for this purpose. The synthesis method developed here allows us to determine the dimensions of a four-link planar mechanism in order to regulate the spring extension in such a way that the output force at the cable drum is approximately constant. The synthesis method is classified among those defined in terms of a reduced number of design parameters. The set of design parameters is the same for a wide class of four-link planar mechanisms. Nonetheless, the four-bar linkage is taken as the example to illustrate the method. The effectiveness of the method is demonstrated on the basis of comparison with two known approaches, including one in which the number of design parameters is not reduced.

Systematic use of velocity and acceleration coefficients in the kinematic analysis of single-DOF planar mechanisms

In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage (i.e., a mechanism containing only lower pairs), complex numbers are an easy-to-use tool for writing linkage's loop equations that are formally differentiable and are the only constraint equations of linkages. Actually, the use of complex numbers for systematically writing the constraint equations of planar mechanisms is often limited to linkages. The possible presence of higher pairs in these mechanisms is usually managed through either equivalent linkages or apparent velocity/acceleration equations. Both these methods are simple to implement for a single mechanism configuration, but become cumbersome when continuous motion has to be analyzed. Other approaches use ad hoc auxiliary equations. Here, first, a general notation that brings to select particular auxiliary equations is proposed; then, such notation is adopted to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar mechanisms. The proposed notation and algorithm, over being efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, are easy to present planar kinematics, with the complex-number method extended to higher pairs, in graduate and/or undergraduate courses.

Tolerance Analysis of Planar Mechanisms Based on a Residual Approach: A Complementary Method to DLM

The kinematic performance of mechanisms is affected by different uncertainty sources involved in the manufacturing and assembling cycle; among these are the geometric variations. It is known that the effects of these variations produce position errors which are not usually included in the design process. With this objective, a complementary method for the tolerance analysis of planar mechanisms that incorporate geometric variations is presented in this paper. The approach is based on Direct Linearization Method (DLM) that does not consider all the kinematically admissible solutions. DLM naturally minimizes a residual functional H; however it is possible to maximize the residual by means of a proposed complementary method called H-Based Residual Method (RMH). From the proposed methodology, local and global error domains can be defined to predict the maximum and minimum position errors caused by the input variations. DLM and RMH were applied in a four-bar mechanism with dimensional and angular variations to estimate positioning errors. The results show intervals where output positions were invariant with respect to angular variations of the crank. These computations were performed through a distance ratio established with the output deviations determined with nominal angular variations. Furthermore, domain errors were predicted for a set of positions generated by a multivariate normal random algorithm with 1000 combinations of input variations (links lengths). These domains delimited all solutions created in each position stage. It means that by applying the proposed methodology it is possible to estimate the geometric errors of any combination of variations.

Kinetostatic and dynamic analyses of planar compliant mechanisms via a two-port dynamic stiffness model

Serial-parallel configurations are widely designed in compliant mechanisms. In this paper, the transfer matrix method is combined with D'Alembert's principle to develop a two-port dynamic stiffness model for analyzing the kinetostatics and dynamics of complex compliant mechanisms with serial-parallel configurations. In detail, two kinds of improved transfer matrices for parallel sub-chains are derived in a unified form by summarizing the common serial-parallel substructures in compliant mechanisms. Then, a two-port dynamic stiffness model describing the frequency-dependent input and output force-displacement relationship of compliant mechanisms is established. Based on the two-port dynamic stiffness model, procedures for solving the static and dynamic performances of compliant mechanisms are presented. The proposed approach is demonstrated by calculating the displacement amplification ratio, input/output stiffness, natural frequencies and forced dynamic response of two typical precision flexure manipulators. The advantage of the proposed approach lies in its capability to describe the simultaneous kinetostatics and dynamics for a large class of serial-parallel configurations with very few degrees of freedom (DOFs), differing from the previous Lagrange-based dynamic modeling methods in the context of compliant mechanisms and should be of interest to designers.

Error Space Estimation of Three Degrees of Freedom Planar Parallel Mechanisms

Abstract This paper develops a geometric method to estimate the error space of 3-DOF planar mechanisms with the Minimum Volume Ellipsoid Enclosing (MVEE) approach. Both the joint clearances and actuator errors are considered in this method. Three typical planar parallel mechanisms are used to demonstrate. Error spaces of their serial limbs are analyzed. Thereafter, limb-error-space-constrained mobility of the manipulator, namely, the manipulator error space is analyzed. The MVEE method has been applied to simplify the constraint modeling. A closed-form expression for the manipulator error space is derived. The volume of the manipulator error space is numerically estimated. The approach in this paper is to develop a geometric error analysis method of parallel mechanisms with clear algebraic expressions. Moreover, no forward kinematics computations have been performed in the proposed method, in contrast to the widely used interval analysis method. Although the estimated error space is larger than the actual one, because the enclosing ellipses enlarge the regions of limb error space, the method has an attractive advantage of high computational efficiency.

Design of Planar Large-Deflection Compliant Mechanisms With Decoupled Multi-Input-Output Using Topology Optimization

This paper presents a method for topology optimization of large-deflection compliant mechanisms with multiple inputs and outputs by considering the coupling issue. First, the objectives of the design problem are posed by modeling the output loads using several springs to enable control of the input–output behavior. Second, a scheme is proposed to obtain a completely decoupled mechanism. Both input coupling and output coupling are considered. Third, with the implementation of an energy interpolation scheme to stabilize the numerical simulations, the geometrical nonlinearity is considered to appropriately capture the large displacements of compliant mechanisms. Finally, several numerical examples are presented to demonstrate the validity of the proposed method. Comparison studies with the obtained results without considering the coupling issues are also presented.

Optimization of planar mechanisms by using a minimum distance function

The paper examines the application of a general minimum distance error function to the dimensional kinematic synthesis of bidimensional mechanisms. The minimum distance approach makes it possible to solve the problem maintaining the same generality as that of the minimum deformation energy method while solving the problems that occasionally appear in the former method involving low stiffness mechanisms. It is a general method that can deal both with unprescribed and prescribed timing problems, and is applicable for path generation problems, function generation, solid guidance, and any combination of the aforementioned requirements as introduced in the usual precision point scheme. The method exhibits good convergence and computational efficiency. The minimum distance error function is solved with a sequential quadratic programming (SQP) approach. In the study, the synthesis problem is also optimized by using SQP, and the function can be easily adapted to other methods such as genetic algorithms.In the study, the minimum distance approach is initially presented. Subsequently, an efficient SQP method is developed by using analytic derivatives for solving. The next point addresses the application of the concept for the synthesis of mechanisms by using an SQP approach with approximate derivatives. This delivers a situation where the optimization is performed on an error function that itself consists of an inner optimization function. A few examples are presented and are also compared with the minimum deformation energy method. Finally, a few conclusions and future studies are discussed.

A 3D Atlas of Hematopoietic Stem and Progenitor Cell Expansion by Multi-dimensional RNA-Seq Analysis

In vertebrates, hematopoiesis occurring in different niches is orchestrated by intrinsic and extrinsic regulators. Previous studies have revealed numerous linear and planar regulatory mechanisms. However, a multi-dimensional transcriptomic atlas of any given hematopoietic organ has not yet been established. Here, we use multiple RNA sequencing (RNA-seq) approaches, including cell type-specific, temporal bulk RNA-seq, invivo GEO-seq, and single-cell RNA-seq (scRNA-seq), to characterize the detailed spatiotemporal transcriptome during hematopoietic stem and progenitor cell (HSPC) expansion in the caudal hematopoietic tissue (CHT) of zebrafish. Combinatorial expression profiling reveals that, in the CHT niche, HSPCs and their neighboring supporting cells are co-regulated by shared signaling pathways and intrinsic factors, such as integrin signaling and Smchd1. Moreover, scRNA-seq analysis unveils the strong association between cell cycle status and HSPC differentiation. Taken together, wereport a global transcriptome landscape that provides valuable insights and a rich resource to understand HSPC expansion in an intact vertebrate hematopoietic organ.

Dynamic Modeling and Response Analysis of a Planar Rigid-Body Mechanism With Clearance

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

Using servo-drives to optimize the transmission angle of cam mechanisms

Cam mechanisms are widely used in production and handling technology. The common synthesis process of cam mechanisms postulates a constant input motion. Taking into account the properties of cam mechanisms such as the transmission behavior or the installation space, a constant input motion in most cases is not the optimal solution. Accordingly, a method to optimize such properties of cam mechanisms by variation of the input motion is described. The focus of this paper lies on increasing the minimal transmission angle of planar rotary cam mechanisms using a non-uniform input speed. The specialty of this consideration is that the output motion provided by a follower remains unchanged. For the mathematical description of the input motion trajectory, 2D B-Spline curves are used in order to choose control points more intelligently. Moreover, a similar method for flat followers is presented. There, the approach is used to realize output motions that were not possible by actuation of the cam disc with a constant input speed due to invalid cam curvatures.

Topology Optimization of Planar Gear-Linkage Mechanisms.

Topology optimization for mechanism synthesis has been developed for the simultaneous determination of the number and dimension of mechanisms. However, these methods can be used to synthesize linkage mechanisms that consist only of links and joints because other types of mechanical elements such as gears cannot be simultaneously synthesized. In this study, we aim to develop a gradient-based topology optimization method which can be used to synthesize mechanisms consisting of both linkages and gears. For the synthesis, we propose a new ground model defined by two superposed design spaces: the linkage and gear design spaces. The gear design space is discretized by newly proposed gear blocks, each of which is assumed to rotate as an output gear, while the linkage design space is discretized by zero-length-spring-connected rigid blocks. Another set of zero-length springs is introduced to connect gear blocks to rigid blocks, and their stiffness values are varied to determine the existence of gears when they are necessary to produce the desired path. After the proposed topology-optimization-based synthesis formulation and its numerical implementation are presented, its effectiveness and validity are checked with various synthesis examples involving gear-linkage and linkage-only mechanisms.

A 3D Atlas of Hematopoietic Stem and Progenitor Cell Expansion by Multi-Dimensional RNA-Seq Analysis

In vertebrates, hematopoiesis occurring in different niches is orchestrated by intrinsic and extrinsic regulators, which are indispensable for the maintenance of homeostasis in a whole organism. Previous studies have revealed a large number of linear and planar regulatory mechanisms. However, a multi-dimensional transcriptomic atlas of any given hematopoietic organ has not been yet established. Here, we use multiple RNA-seq approaches, including cell type-specific temporal bulk RNA-seq, in vivo GEO-seq, and single-cell RNA-seq (scRNA-seq), to characterize the detailed spatiotemporal transcriptome during hematopoietic stem and progenitor cell (HSPC) expansion in the caudal hematopoietic tissue (CHT) of zebrafish. Combinatorial expression profiling reveals that in the CHT niche, HSPCs and their neighboring supporting cells are co-regulated by shared signaling pathways and intrinsic factors, such as integrin signaling and Smchd1. Moreover, scRNA-seq analysis unveils the strong association between cell cycle status and HSPC differentiation. Taken together, we report a global transcriptome landscape that provides valuable insights and a rich resource for understanding HSPC development, particularly on HSPC expansion in an intact hematopoietic organ. The key signaling pathways and factors identified here would contribute to HSPC expansion in vitro.

A Machine Learning Approach to Kinematic Synthesis of Defect-Free Planar Four-Bar Linkages

Synthesizing circuit-, branch-, or order-defects-free planar four-bar mechanism for the motion generation problem has proven to be a difficult problem. These defects render synthesized mechanisms useless to machine designers. Such defects arise from the artificial constraints of formulating the problem as a discrete precision position problem and limitations of the methods, which ignore the continuity information in the input. In this paper, we bring together diverse fields of pattern recognition, machine learning, artificial neural network, and computational kinematics to present a novel approach that solves this problem both efficiently and effectively. At the heart of this approach lies an objective function, which compares the motion as a whole thereby capturing designer's intent. In contrast to widely used structural error or loop-closure equation-based error functions, which convolute the optimization by considering shape, size, position, and orientation of the given task simultaneously, this objective function computes motion difference in a form, which is invariant to similarity transformations. We employ auto-encoder neural networks to create a compact and clustered database of invariant motions of known defect-free linkages, which serve as a good initial choice for further optimization. In spite of highly nonlinear parameters space, our approach discovers a wide pool of defect-free solutions very quickly. We show that by employing proven machine learning techniques, this work could have far-reaching consequences to creating a multitude of useful and creative conceptual design solutions for mechanism synthesis problems, which go beyond planar four-bar linkages.

Application of Screw Theory to the Analysis of Instant Screw Axis of Vehicle Suspension System

This paper proposes a method using screw theory to find the twist of a rigid body of a mechanism. For this, a geometric method to determine the screws and reciprocal screws associated with kinematic joints and links is introduced. This geometric method provides a simple way to find the wrenches acting upon a rigid body of a mechanism using the joint types and positions. Then, the twist which is reciprocal to the wrenches is determined to find the instant screw axis and pitch of the body. The proposed method is applied to planar mechanisms and spatial suspension mechanisms. For planar mechanisms, the method finds the instant center of velocity as the point in the plane of planar motion intersected by the instant screw axis. Using the proposed method, the instant screw axes and pitches are determined for the bump-rebound motion and steering motion of the double wishbone, McPherson strut, and 5-SS multi-link type suspension mechanisms. The numerical results agree with findings of previous researches.