Deformation Transition Graphs in Forming Operations of Rheological Objects

1 I n t r o d u c t i o n In food industry, we can find many manipulative operations that deal with deformable rheologic materials such as dough, paste, jelly, and meat. Most these operations are done by humans. Especially, operations with large deformation of rheologic objects depend upon humans. For example, forming of pizza dough to a thin circular shape is performed by humans while extension of the dough can be done by mechanical stretchers. Thus, automatic operations by machines are strongly required for the purpose of cost reduction and cleanness of food. Modeling of viscoelastic objects has been studied in computer graphics [1, 2] and virtual reality [3]. These researches focus on the deformation modeling of viscoelastic objects and forming operations of viscoelastic objects are out of consideration. Thus, we have no method to determine a forming strategy based on the object model. Material nature of rheologic objects is investigated extensively in rheology [4]. Unfortunately, deformation of rheologic objects in 3D space is not studied in theology. Handling operations of deformable objects have been studied recently. Automatic handling of deformable parts in garment industry and shoe industry has been experimentally studied [5]. Zheng and Chen have proposed a strategy to insert a deformable beam into a hole [6]. Wada et al. have propose a control law for the positioning operation of extensible clothes [7]. These researches focus 0 7 8 0 3 5 8 8 6 4 / 0 0 / $ 1 0 . 0 0 © 2000 IEEE 307 obot ics , u , Shiga 525-8577, J a p a n se . r i t sumei . ac . jp on handling of elastic objects and forming operations of theologic objects are out of focus. In this paper, we will focus on the automatic forming operation of rheologic objects. First, we will develop a prototype of a forming machine with multi degrees of freedom. Second, we will introduce a deformation transition graph so that the forming process can be described. We will then develop a method to generate the deformation transition graph through experiments. Finally, we will explain a forming control method of a theological object based on the deformation transition graph. 2 D e s i g n o f Forming Machine w i t h M u l t i D e g r e e s o f F r e e d o m In this section, we will propose a novel forming machine with multi degrees of freedom for rheological objects. Traditional mechanical stretchers can extend a rheological object using a roller and a table. It is, however, difficult to form a rheological object by a mechanical stretcher, where the configuration between a roller and a table is fixed. This is caused by viscoelastic nature of a rheological object, which yields its deformation during the forming process. Moreover, physical properties including elasticity and viscosity often change during the forming process. Consequently, it is required to control the configuration between a roller and a table to perform forming process of rheological objects successfully. Let us investigate the configuration between a roller and a table. Figure 1 shows the configuration between a cylindrical roller and a planar table. The roller has six degrees of freedom relative to the table; three for translation and three for rotation. Traditional stretchers have two degrees of freedom; table feed motion T1 and roller rotation R1. Table feed motion in the stretchers is usually provided in one direction. The roller rotates around its central axis to stretch rheological objects. The configuration between a roller and a table is fixed in the stretchers. Let us examine whether the other freedoms change the configuration or not. Translation along the central axis of the roller does not change the configuration. Namely, this freedom is not effective to change the configuration. Translational motion T2, rotational motion R2, and