Topology optimization of planar linkage systems involving general joint types

Kang, Seok‐Won; Kim, Suh In; Kim, Yoon Young

doi:10.1016/j.mechmachtheory.2016.05.015

Cited by 28 publications

(7 citation statements)

References 32 publications

(80 reference statements)

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“…To define the mean value of the work transmittance efficiency function

\overset{η}{true}

in Formulation A,

F_{t *}^{ext}

must be applied to the system. Among various choices of

F_{t *}^{ext}

to make

W_{t *}^{out}

nonzero, the following form is selected as in previous studies:

F_{t *}^{ext} = F_{0} \frac{{\{{\overset{falsê}{q}}_{x, t^{*} - 1}, {\overset{falsê}{q}}_{y, t^{*} - 1}, 0\}}^{T} - {\{{\overset{falsê}{q}}_{x, t^{*}}, {\overset{falsê}{q}}_{y, t^{*}}, 0\}}^{T}}{‖{({},,, {\overset{q}{true}}_{x, {italict}^{*} - 1}, {\overset{q}{true}}_{y, {italict}^{*} - 1}, 0)}^{T} - {({},,, {\overset{q}{true}}_{x, {italict}^{*}}, {\overset{q}{true}}_{y, {italict}^{*}}, 0)}^{T}‖},

where F 0 = 1 N. To ensure that the desired path of the wheel center is traced accurately, we choose the error bounds for constraint equations as ε (1) = ε (2) = 1 mm and ε (3) = ε (4) = ε (5) = 0.02 ∘ .…”

Section: Suspension Mechanism Synthesis By the Proposed Methodsmentioning

confidence: 99%

“…Kawamoto proposed a ground model consisting of nonlinear bar elements for the topology optimization–based synthesis of planar linkage mechanisms. An alternative modeling method is to use spring‐connected rigid blocks (SBs) . Whether bar elements or spring‐connected rigid blocks are used to make a ground model, mechanism layout determinations, which are discrete in nature, are expressed in terms of continuous design variables since a gradient‐based optimizer cannot be used otherwise.…”

Section: Introductionmentioning

confidence: 99%

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Topology optimization of vehicle rear suspension mechanisms

Kim

Kang

et al. 2017

Numerical Meth Engineering

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As suspensions critically affect the ride and handling performance of vehicles, considerable efforts have been made to improve their design by an optimization method. In this paper, we propose a topology optimization-based method for suspension synthesis by using a 3-dimensional model constructed with nonlinear bars and zero-length springs that discretize the 3-dimensional space between the chassis frame and a vehicle wheel. For optimization, bar cross-sections and spring stiffness values are used as design variables alongside the nodal positions of bar elements as shape optimization variables to simultaneously optimize the topology and shape. To verify the proposed approach, 2 types of design problems were solved: recovering known suspension mechanisms for a given set of wheel trajectories and synthesizing unknown suspension mechanisms that satisfy several design constraints typically used in the automobile industry. Through these examples, possibilities to design new and advanced suspensions by the proposed optimization method are clearly demonstrated. in a reasonable amount of time. Therefore, we hope to set up the topology optimization problem for suspension synthesis by using a numerically efficient gradient-based optimizer.Although there is no study or report that uses the topology optimization method for 3-dimensional vehicle suspension systems, there were earlier studies that dealt with planar linkage mechanisms by topology optimization. To synthesize 3-dimensional suspension systems, a recently proposed energy-based formulation developed for planar mechanisms 5 will be expanded by first reviewing earlier studies that discussed issues and difficulties with rigid body mechanism synthesis using the topology optimization method.Kawamoto 6 proposed a ground model consisting of nonlinear bar elements for the topology optimization-based synthesis of planar linkage mechanisms. An alternative modeling method is to use spring-connected rigid blocks (SBs). 7-9 Whether bar elements or spring-connected rigid blocks are used to make a ground model, mechanism layout determinations, which are discrete in nature, are expressed in terms of continuous design variables since a gradient-based optimizer cannot be used otherwise. As explained below, continuous variables cause major issues even though they cannot be avoided for efficient calculations. Besides aforementioned studies, other relevant studies 10-16 were reported. However, realistic problems appearing in engineering applications could not be solved until recently because of the discrete-type DOF (degree of freedom) constraint, which is something a rigid body mechanism must satisfy. This is not easy to express in the differentiable form when continuous design variables are used to develop a gradient-based topology optimization method. If a mechanism with a single input and a single output is to be synthesized, its DOF should be exactly 1. It is only recently that the DOF issue has been resolved by Kim and Kim 5 for the planar linkage mechanism synthesis by showing th...

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“…To define the mean value of the work transmittance efficiency function

\overset{η}{true}

in Formulation A,

F_{t *}^{ext}

must be applied to the system. Among various choices of

F_{t *}^{ext}

to make

W_{t *}^{out}

nonzero, the following form is selected as in previous studies:

F_{t *}^{ext} = F_{0} \frac{{\{{\overset{falsê}{q}}_{x, t^{*} - 1}, {\overset{falsê}{q}}_{y, t^{*} - 1}, 0\}}^{T} - {\{{\overset{falsê}{q}}_{x, t^{*}}, {\overset{falsê}{q}}_{y, t^{*}}, 0\}}^{T}}{‖{({},,, {\overset{q}{true}}_{x, {italict}^{*} - 1}, {\overset{q}{true}}_{y, {italict}^{*} - 1}, 0)}^{T} - {({},,, {\overset{q}{true}}_{x, {italict}^{*}}, {\overset{q}{true}}_{y, {italict}^{*}}, 0)}^{T}‖},

Section: Suspension Mechanism Synthesis By the Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topology optimization of vehicle rear suspension mechanisms

Kim

Kang

et al. 2017

Numerical Meth Engineering

Self Cite

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“…That is undoubtedly the case of the technique for creating idealized bolts with the topological derivative approach proposed by Rakotondrainibe et al [247] in a Renault associated research. Other examples can be found in the synthesis method for mechanisms proposed by Kang et al [436] with a possible application to the pinned and sliding joints in structures.…”

Section: Joints Detailingmentioning

confidence: 99%

Topology Optimisation in Structural Steel Design for Additive Manufacturing

2021

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Topology Optimisation is a broad concept deemed to encapsulate different processes for computationally determining structural materials optimal layouts. Among such techniques, Discrete Optimisation has a consistent record in Civil and Structural Engineering. In contrast, the Optimisation of Continua recently emerged as a critical asset for fostering the employment of Additive Manufacturing, as one can observe in several other industrial fields. With the purpose of filling the need for a systematic review both on the Topology Optimisation recent applications in structural steel design and on its emerging advances that can be brought from other industrial fields, this article critically analyses scientific publications from the year 2015 to 2020. Over six hundred documents, including Research, Review and Conference articles, added to Research Projects and Patents, attained from different sources were found significant after eligibility verifications and therefore, herein depicted. The discussion focused on Topology Optimisation recent approaches, methods, and fields of application and deepened the analysis of structural steel design and design for Additive Manufacturing. Significant findings can be found in summarising the state-of-the-art in profuse tables, identifying the recent developments and research trends, as well as discussing the path for disseminating Topology Optimisation in steel construction.

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“…A novel technique of double-springs was introduced by Kang et al [2] to attach a finite number of ground rectangular rigid blocks. Revolute joints and P-pairs were used by Mitsi et al [3][4][5] in position analysis of the Assur group.…”

Section: Introductionmentioning

confidence: 99%

Automatic Generation of N-Bar Planar Linkages Containing Sliders

Helal

Eleashy

2021

Applied Sciences

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In this work, a generalized algorithm is introduced to generate all alternatives of planar N-bar kinematic chains (KCs) with simple joints containing sliders. A simple graphical technique is introduced to enumerate all available N-bar chains with prismatic (P) joints. Then, a new topological Loop Code (TLC) is presented to detect isomorphic chains during the enumeration process in addition to detecting rejected KCs. A visual C++ code is developed for automatic enumeration and detection of rejected KCs and isomorphic KCs. Examples of 6, 8, and 10-bar KCs are presented to illustrate algorithm procedures. As a result, 21, 16, and 1350 KCs have P-joints for Stephenson, Watt, and 8-bar chains, respectively. Also, 308 KCs are obtained for a 10-bar KC with up to 3 sliders.

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Topology optimization of planar linkage systems involving general joint types

Cited by 28 publications

References 32 publications

Topology optimization of vehicle rear suspension mechanisms

Topology optimization of vehicle rear suspension mechanisms

Topology Optimisation in Structural Steel Design for Additive Manufacturing

Automatic Generation of N-Bar Planar Linkages Containing Sliders

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