A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis

Chou, Yueh Ching; Chandru, V.; Barash, Moshe M.

doi:10.1115/1.3188764

Cited by 203 publications

(106 citation statements)

References 12 publications

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“…Beberapa penelitian sebelumnya yang membahas ini diantaranya adalah Asada dan By [1] yang mengembangkan model kinematik penetap. 1 Chou et al [2] menerapkan teori ulir (screw theory) dalam merumuskan keseimbangan penetap untuk benda-kerja prismatik kaku, dalam upaya mendapatkan gaya klem yang fisibel. Ariastuti et al [3] menggunakan model Chou untuk mendapatkan koordinat lokator dan klem, dengan cara memeriksa fisibilitas keseimbangan gaya dan momen dari koordinat lokator dan klem.…”

Section: Pendahuluanunclassified

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Model Optimasi Fixturing Benda-kerja dengan Prinsip 3-2-1 Klem Tunggal

Toha

Diratama

Wigenaputra

2017

jti

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Abstract:To hold a workpiece firmly at its place, a fixture is required. Some previous studies have discussed the balance of forces and moments that are based on kinematic model, screw theory, contact force and position error. The most fundamental problem in the design of the fixture is to determine the coordinates of a locator and clamp and a clamping force, so that the workpiece is stable during the machining process. This paper discusses an optimization model to determine the coordinates of the locator and clamp and the clamping force, focusing to the balance of forces and moments. Specifically, the optimization model developed is used for solving the problem of fixturing the workpiece applying the 3-2-1 principle. Numerical examples are given to illustrate the application of the model. The optimization model is solved using standard nonlinear programming software.Keywords: Fixture, force, moment, locator, clamp, optimization. PendahuluanPenetap (fixture) merupakan alat bantu yang digunakan pada pemesinan, perakitan, inspeksi, dan berbagai operasi manufaktur lainnya. Dalam proses pemesinan, benda-kerja akan mengalami gaya dan momen pemotongan, sehingga diperlukan penetap untuk memegang benda-kerja agar diam pada tempatnya. Hal ini diperlukan agar bendakerja hasil pemesinan sesuai dengan spesifikasi desainnya. Penetap terdiri dari lokator dan klem. Lokator berperan untuk menjaga benda-kerja berada pada tempatnya, sedangkan klem berperan untuk menghilangkan pergerakan yang terjadi, dengan memberikan gaya yang akan melawan pergerakan benda-kerja.Suatu benda-kerja pada ruang tiga dimensi, dapat bergerak pada dua-belas arah (memiliki dua-belas derajat kebebasan). Penetapan (fixturing) dengan prinsip 3-2-1 menempatkan tiga lokator bawah, dua lokator samping, dan satu lokator pada samping lainnya, sehingga benda-kerja hanya memiliki tiga derajat kebebasan. Untuk memegang benda kerja pada tempatnya (nol derajat kebabasan), digunakan satu klem atas, satu klem samping, dan satu klem samping lainnya, yang masing-masing berlawanan dengan arah lokator.Untuk memegang benda-kerja pada tempatnya, diperlukan analisis keseimbangan gaya dan momen yang terjadi. Beberapa penelitian sebelumnya yang membahas ini diantaranya adalah Asada dan By [1] yang mengembangkan model kinematik penetap.

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Section: Pendahuluanunclassified

“…Koordinat dan besarnya gaya pemesinan adalah . Besarnya gaya klem , 2 , lebih kecil dari gaya klem yang ditentukan.…”

Section: Hasil Dan Pembahasan Contoh Numerikunclassified

Model Optimasi Fixturing Benda-kerja dengan Prinsip 3-2-1 Klem Tunggal

Toha

Diratama

Wigenaputra

2017

jti

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“…The parameters and are positive constants while is a positive constant in compressive fixtures where the fixels push toward the concurrency point. 6 Assuming compressive fixtures, is positive when is strictly positive. Since is the sum of the preloading forces, the requirement implies that the fixels must be preloaded for stability.…”

Section: B Minimum Deflection Fixtures Using Three Fixelsmentioning

confidence: 99%

“…Fixturing plays an important role in manufacturing and assembly applications [6], [35], [47]. In these applications, a workpiece is fixtured with some preloading forces by fixturing elements, or fixels.…”

Section: Introductionmentioning

confidence: 99%

Constructing minimum deflection fixture arrangements using frame invariant norms

Lin

Burdick

Rimon

2006

IEEE Trans. Automat. Sci. Eng.

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Abstract-This paper describes a fixture planning method that minimizes object deflection under external loads. The method takes into account the natural compliance of the contacting bodies and applies to two-dimensional and three-dimensional quasirigid bodies. The fixturing method is based on a quality measure that characterizes the deflection of a fixtured object in response to unit magnitude wrenches. The object deflection measure is defined in terms of frame-invariant rigid body velocity and wrench norms and is therefore frame invariant. The object deflection measure is applied to the planning of optimal fixture arrangements of polygonal objects. We describe minimum-deflection fixturing algorithms for these objects, and make qualitative observations on the optimal arrangements generated by the algorithms. Concrete examples illustrate the minimum deflection fixturing method.Note to Practitioners-During fixturing, a workpiece needs to not only be stable against external perturbations, but must also stay within a specified tolerance in response to machining or assembly forces. This paper describes a fixture planning approach that minimizes object deflection under applied work loads. The paper describes how to take local material deformation effects into account, using a generic quasirigid contact model. Practical algorithms that compute the optimal fixturing arrangements of polygonal workpieces are described and examples are then presented.

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“…However, in many grasping applications, the natural compliance of the contacting bodies plays an important role. Consider, for example, fixturing for manufacturing or assembly [5], [23], [33]. In these applications, a workpiece is fixtured with some preloading forces by several fixturing elements (or fixels).…”

mentioning

confidence: 99%

Computation and Analysis of Natural Compliance in Fixturing and Grasping Arrangements

Lin

Burdick²,

Rimon³

2004

IEEE Trans. Robot.

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Abstract-This paper computes and analyzes the natural compliance of fixturing and grasping arrangements. Traditionally, linear-spring contact models have been used to determine the natural compliance of multiple contact arrangements. However, these models are not supported by experiments or elasticity theory. We derive a closed-form formula for the stiffness matrix of multiple contact arrangements that admits a variety of nonlinear contact models, including the well-justified Hertz model. The stiffness matrix formula depends on the geometrical and material properties of the contacting bodies and on the initial loading at the contacts. We use the formula to analyze the relative influence of first-and second-order geometrical effects on the stability of multiple contact arrangements. Second-order effects, i.e., curvature effects, are often practically beneficial and sometimes lead to significant grasp stabilization. However, in some contact arrangements, curvature has a dominant destabilizing influence. Such contact arrangements are deemed stable under an all-rigid body model but, in fact, are unstable when the natural compliance of the contacting bodies is taken into account. We also consider the combined influence of curvature and contact preloading on stability. Contrary to conventional wisdom, under certain curvature conditions, higher preloading can increase rather than decrease grasp stability. Finally, we use the stiffness matrix formula to investigate the impact of different choices of contact model on the assessment of the stability of multiple contact arrangements. While the linear-spring model and the more realistic Hertz model usually lead to the same stability conclusions, in some cases, the two models lead to different stability results.

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A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis

Cited by 203 publications

References 12 publications

Model Optimasi Fixturing Benda-kerja dengan Prinsip 3-2-1 Klem Tunggal

Model Optimasi Fixturing Benda-kerja dengan Prinsip 3-2-1 Klem Tunggal

Constructing minimum deflection fixture arrangements using frame invariant norms

Computation and Analysis of Natural Compliance in Fixturing and Grasping Arrangements

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