Rigid-body Linkages Research Articles

Simultaneous Shape and Topology Optimization of Planar Linkage Mechanisms Based on the Spring-Connected Rigid Block Model

Abstract Using the topology optimization can be an effective means of synthesizing planar rigid-body linkage mechanisms to generate desired motion, as it does not require a baseline mechanism for a specific topology. While most earlier studies were mainly concerned with the formulation and implementation of topology optimization-based synthesis in a fixed grid, this study aims to realize the simultaneous shape and topology optimization of planar linkage mechanisms using a low-resolution spring-connected rigid block model. Here, we demonstrate the effectiveness of simultaneous optimization over a higher-resolution fixed-grid rigid block-based topology optimization process. When shape optimization to change the block shapes is combined with topology optimization to synthesize the mechanism, the use of low-resolution discretized models improves the computation efficiency considerably and helps to yield compact mechanisms with less complexity, making them more amenable to fabrication. After verifying the effectiveness of the simultaneous shape and topology optimization process with several benchmark problems, we apply the method to synthesize a mechanism which guides a planar version of a human's gait trajectory.

Nonlinear behaviour design using the kinematic singularity of a general type of double-slider four-bar linkage

Kinematic singularities existing in rigid-body linkages are applied to design the mechanism with nonlinear (stiffness) behaviours. The kinematic singularities of a general type of double-slider four-bar linkage, whose two paths of the sliders are not perpendicular, are identified by analysing the kinematic formulation. A new type of mechanism is synthesized by placing translational springs and torsional springs at corresponding joints. Two motion models are proposed to design the different types of nonlinear behaviours. After constructing the force-displacement formulation of the mechanism, four types of nonlinear behaviours including the bistable behaviour, the partial negative stiffness behaviour, the partial zero-stiffness behaviour and the positive stiffness behaviour are investigated. The influences of designed parameters including spring stiffness, geometry parameters, and initial input position on nonlinear characteristics are illustrated. The results indicate that the mechanism exhibits corresponding nonlinear behaviours with these different parameters. A method of generating an expected nonlinear behaviour over a range of input displacement is developed, with a particular emphasis on the constant-force behaviour. The approach of designing the nonlinear behaviour based on the rigid-body linkages with springs expands the application range of the kinematic singularities of rigid-body linkages, and can also be employed to construct nonlinear compliant mechanisms.

CAE Supported Sustainable Product Development - Case Study of Compact Flow Guiding with Flame Lift Mechanism

The flame device design process and lift mechanism concerns were investgated. Combine qualitative and CAE simulation were proposed to fulfill its functions. Redesign structures allow the user to add fuel and cleaning base parts safely. For enhancing usability, airflow guidance structure cannot tolerate interference with the fuel intake. Within space constrain, we changed guidance channel to produce an ornamental flame with acceptable flame height. The cover is movably engaged with the base and selectively closes the opening. The lift mechanism comprises a supporting member and bearing allow moving to the predetermined height. Rigid body linkage and flow field simulated enables fine tune of geometric design. Functional test and measurement are carried out to confirm the product features. The measured average temperature of the metal chassis is 37.25 °C and that of glass is 141°C. The result shows successful simplicity mechanism and low surface temperature design.

Application of Rigid-Body-Linkage Static Balancing Techniques to Reduce Actuation Effort in Compliant Mechanisms

There are analytical methods in the literature where a zero-free-length spring-loaded linkage is perfectly statically balanced by addition of more zero-free-length springs. This paper provides a general framework to extend these methods to flexure-based compliant mechanisms through (i) the well know small-length flexure model and (ii) approximation between torsional springs and zero-free-length springs. We use first-order truncated Taylor's series for the approximation between the torsional springs and zero-free-length springs so that the entire framework remains analytical, albeit approximate. Three examples are presented and the effectiveness of the framework is studied by means of finite-element analysis and a prototype. As much as 70% reduction in actuation effort is demonstrated. We also present another application of static balancing of a rigid-body linkage by treating a compliant mechanism as the spring load to a rigid-body linkage.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

How to Choose From a Synthesized Set of Path-Generating Mechanisms

Partially compliant mechanisms inherit the attributes of fully compliant and rigid-body linkages and offer simpler, compact design alternatives to accomplish complex kinematic tasks such as tracing large nonsmooth paths. This paper describes qualitative and quantitative criteria that can be employed to select the linkage configuration. The proposed criteria are categorized as general or specific. General criteria pertain to often-used kinematic attributes whereas specific criteria address the application at hand. The veracity and viability of each mechanism are evaluated with respect to compactness, design simplicity, static and dynamic failure, number of rigid-body joints, relative ease of fabrication, and other relevant criteria. Three decision-making techniques, namely, Pugh decision matrix, analytic hierarchy process, and a variant of the Pugh decision matrix are used to perform the evaluation. An example of a displacement-delimited gripper with a prescribed large nonsmooth path is used to illustrate linkage selection.

A complex solution framework for the kinetostatic synthesis of a compliant four-bar mechanism

This paper presents a systematic solution framework for the kinetostatic synthesis of compliant four-bar mechanisms. The goal of the kinetostatic synthesis is to find feasible compliant mechanism solutions for a given set of kinematic and force/energy specifications. Similar to the synthesis of rigid body linkages, we first classify kinetostatic synthesis problems into three major categories: function, motion and path generations. The kinetostatic synthesis equations are derived by combining the kinematic synthesis and static equilibrium equations. We then propose a comprehensive framework based on polynomial solvers for obtaining solutions to these synthesis equations. When kinematic and static equations are decoupled, we solve first kinematic equations independently and then solve static equations for springs' stiffness. While they are coupled, we transform them into a polynomial form and solve them simultaneously with polynomial solvers. For this case a parameter continuation is devised to avoid computing for the junk solutions. At last, three representative examples are provided to demonstrate the solution process and verify the solution framework.

Kempe’s linkages and the Universality Theorem

Inspired by James Watt’s approximate straight line generator, kinematicians of the 19th century challenged themselves to design a mechanical device that could convert rotary motion into a perfect straight line and vice versa. Few inventions emerged in 1864 due to Peaucellier and Lipkin and in 1875 due to Hart. Just a year later, in 1876, Alfred B Kempe presented a generalized method for linkages that could exactly trace any algebraic curve of degree n and not just a straight line. This work of Kempe is of classical importance. Yet, many are not aware of it perhaps because the resulting linkages are quite complex. This article discusses Kempe’s method that highlights the way he treated the rotations analytically using only parallelograms and contra-parallelograms to get the final rigidbody linkage tracing a given algebraic curve. An elaborate example with geometric construction using only a ruler and compass is presented to help the readers understand the assembly of Kempe’s linkages.

Multibody Model of an Ornithopter

and feedback control techniques. Analysis of inertial properties and previous ight data has led to the development of a multibody model, where the ornithopter is modeled as a collection of chains of rigid body linkages emanating from a central fuselage. The Boltzmann-Hamel equations of motion are employed to generate a state space model which is cast into a form canonical to the nonlinear robotics and adaptive control communities. Software implementation of the symbolic derivation and numerical integration of the equations of motion are discussed. Preliminary results are presented for the simulation of the ornithopter in straight and level ight using a simplied aerodynamics model, which illustrate the trends in measured ight data.

Mechanical and geometric advantages in compliant mechanism optimization

This paper presents a focused examination of the mechanical and geometric advantages in compliant mechanisms and their ramifications in the design formulations of compliant mechanisms posed as a topology optimization problem. With a linear elastic structural analysis, we quantify mechanical (and geometric) advantage in terms of the stiffness elements of the mechanism’s structure. We then analyze the common formulations of compliant mechanism optimization and the role of the external springs added in the formulations. It is shown that the common formulations using mechanical (or geometric) advantage would directly emulate at best a rigid-body linkage to the true optimum design. As a result, the topology optimization generates point flexures in the resulting optimal mechanisms. A case study is investigated to demonstrate the resulting trends in the current formulations.

A Kinetoelastic Formulation of Compliant Mechanism Optimization

The current design algorithms for compliant mechanisms often generate solutions that imitate rigid-body linkages by means of point flexures or flexure pivots, by using the popular spring model formulation. This paper presents a kinetoelastic formulation for compliant mechanism optimization. With a state equation of the mechanism defined by the elasticity theory, the model incorporates not only the kinematic function requirements of the mechanism but, more importantly, the necessary conditions on the compliance characteristics of the mechanism’s structure. The kinematics of the compliant mechanism is defined on rigid bodies of input/output ports and is related to a set of kinetoelastic factors of the mechanism’s compliance matrix. The kinetoelastic formulation is applied to the problem of optimizing a compliant translational joint, producing compliant designs with compliance properties such as the leaf spring type sliding joint as opposed to the notch-type joint. This paper represents an initial development toward a more general methodology for compliant mechanism optimization.

Kinematic analysis of linkages based in finite elements and the geometric stiffness matrix

This paper presents a numerical approach to rigid body linkage kinematics, based on a reduced form of the stiffness matrix and in structural analysis concepts. This matrix may be referred to as geometric stiffness matrix, or simply as geometric matrix. It is derived from basic nodes and length constraints, and provides full information on the kinematic properties of any linkage, including positions, velocities, accelerations, jerks and singular positions. This approach offers a number of major advantages, especially where simplicity and generality are concerned. The computational cost is also very low, because of the simplicity of the numerical calculations and the reduced dimensions of the matrices involved.

Dynamic simulation of FES-cycling: influence of individual parameters

Cycling by means of functional electrical simulation (FES) is an attractive training method for spinal cord injured (SCI) subjects. FES-cycling performance is influenced by a number of parameters like seating position, physiological parameters, conditions of surface stimulation, and pedaling rate. The objective of this paper was the determination of the influence of the most important parameters on optimal muscle stimulation patterns and power output of FES-cycling on a noncircular pedal path. The rider-cycle system was modeled as a planar articulated rigid body linkage on which the muscle forces are applied via joint moments and implemented into a forward dynamic simulation of FES-cycling. For model validation, the generated drive torques that are predicted by the simulation were compared to measurements with an individual paraplegic subject. Then, a sensitivity analysis was carried out to determine the influences of the most important parameters for surface stimulation of gluteus maximus, quadriceps, hamstrings, and peroneus reflex. The results show how optimal stimulation patterns and the expected mean active power output can be estimated based on measured individual parameters and adjusted geometry and stimulation parameters for a particular SCI-subject. This can considerably improve FES-cycling performance and relieve the patients by shortening the time that is necessary for experimental adaptation of the stimulation patterns.

Design of Distributed Compliant Mechanisms

The optimization problem formulations currently used to synthesize compliant mechanism topologies aim to maximize the flexibility for obtaining the desired output motion while maximizing the overall stiffness for satisfactorily bearing the applied loads. The best solution to this problem, as posed, is a linkage consisting of rigid members connected together with revolute joints. The current elastic mechanics-based formulations do generate compliant topologies that closely imitate a rigid-body linkage by means of lumped compliance as in flexural pivots. Systematically generating such topology solutions could serve as a creative aid in the conceptual design of mechanisms, especially when the force-deflection specifications are nonintuitive to human designers. However, flexural pivot-based compliant designs are not useful in most applications when large displacements and/or high strength are desired. Ideally, compliant designs should distribute flexibility uniformly throughout the structure rather than limiting it to a few pivots. In this article, we discuss why current formulations often lead to lumped compliant designs, put forth a proper quantitative measure for distributed compliance, and present a novel formulation that guarantees distributed compliant topologies. The method is explained in detail and is illustrated with examples.