IEEE Robotics & Automation Magazine - September 2014 - 97

succeeded in identifying the scaling rules that enable a quick
evaluation of the design implications in scaling up dynamic
flexible sculptures, such as the Len Lye works-see Raine et
al. [4]. Furthermore, Gooch and Raine [5] discovered that
different scaling rules have different effects. Giesbrecht et al.
[6] designed the leg of a well-known kinetic sculpture, a
wind beast [7], using the theory of mechanism design and
genetic algorithms. A prototype of a small wind beast, comprising both mechanical and electrical components, was built
based on the dynamic force analysis. The foregoing works
did apply some engineering and design principles and techniques. However, there is a lack of a general framework upon
which dynamic sculptures can be developed more systematically while not losing artistic flavors.
In this article, we present a new paradigm of creating a
dynamic sculpture along with its technology for the realization of the dynamic sculpture based on the new paradigm.
The new paradigm for dynamic sculpture is to view a
dynamic sculpture as consisting of a backbone and flesh. The
backbone follows the architecture of robots, and the flesh is
any object that can be attached onto the backbone. To implement this concept of a dynamic sculpture, a modular system
made of plastic materials is used, known as a modular plastic
module (MPM), for which any block modular system can be
employed. An example of an MPM is the LEGO block. Note
that the LEGO system follows the so-called sectional interface [8], so its modularity is of the highest degree. This feature makes the LEGO system a good candidate to implement
the new paradigm; in particular, both the backbone and flesh
can be constructed using the LEGO system. Figure 1 shows
several modules of the LEGO MPM system; as such, a
dynamic sculpture in essence becomes an MPM system. In
this article, we present a technique to analyze the characteristics of motion of the MPM system, which is the first step to
designing the dynamic sculpture. The use of the MPM
has an additional benefit, as it virtually provides a new avenue to construct a sculpture. On a historical note, the foregoing paradigm for dynamic sculpture first appeared in [9].
The work presented in this article is a significant extension of
that work.
A fundamental requirement for such a technique is systematization using a computer program to generate the model
and code automatically. This code generation is typically performed by having a computer code for a general analysis procedure based on the availability of a particular formalism,
such as the finite-element method shown in [10] and [11],
and requiring a user to provide a description of the system to
be analyzed through an input file to the code [11]. In the literature relating to robotics, the development of such a technique
may be called automatic kinematic and dynamic analysis [11].
The MPM system is different from the conventional modular robots or machines in the sense that the latter mostly has
serial and parallel structures and there is no rigid joint or connector among the modules. Note that the rigid joint connects
two modules with no relative motion, and its concept was
perhaps first proposed in [12]. Despite these differences, the

Stud

Stud
Inlet

(a)
Pin

Pinhole

(b)
Axle
Hole

Axle

(c)
Figure 1. The interfaces in MPM systems [9]. (a) The stud-
stud inlet interface between two link modules, which forms
fixed connections. (b) The pinhole-pin interface between a
link module and a rotary joint module. (c) The axle hole-axle
interface between a link module and a prismatic joint module.

existing work on the motion analysis of modular robots is
useful to this article and is reviewed in the following.
There has been considerable interest in the automatic modeling of modular robot configurations [13]-[21]. Note that the
complexity of developing a system for the computer generation of the kinematic and dynamic equations depends on the
generality of the modular robot configuration. Chen and Yang
[16], [17] and Chen et al. [18] considered a relatively more
general modular robot architecture, and they addressed the
issue of the automatic kinematic and dynamic modeling for
modular robot configurations based on their architecture
using the product-of-exponentials method. Benhabib et al.
[19] proposed methods to generate kinematic Denvit-Hartenberg (D-H) parameters from the configuration-space representation of robots. Bi et al. [20] and Bi [21] proposed a more
general architecture of modular robots and an approach to determine the kinematics and dynamics of the modular robots
based on the D-H architecture of kinematic representation of
the links and the kinematic pairs.
In our technique, the D-H architecture is used, and, therefore, two challenges in our case are 1) a computational representation of the MPM systems and 2) an algorithm to convert
this computational representation to the D-H representation.
This article will address these two challenges. Finally, this article will present both virtual and physical dynamic sculptures
made using the MPM system.
september 2014

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