Elsevier

Computer-Aided Design

Volume 34, Issue 13, November 2002, Pages 997-1010
Computer-Aided Design

An automatic method for controlling the centre of gravity of a model

https://doi.org/10.1016/S0010-4485(01)00158-0Get rights and content

Abstract

In many applications the location of the centre of gravity of a mechanical part is an important factor that a designer must consider. If it is not in a desired location, a part might not work properly, e.g. unbalanced force might be generated in a rotational part. After a part is modeled, its centre of gravity cannot be altered unless its external shape or internal mass distribution is changed. However, the external shape is usually constrained by other design considerations. In this paper, an algorithm is proposed for controlling the centre of gravity of a hollowed part. Using this algorithm, the location of the centre of gravity of a part is controlled by changing its internal mass distribution.

Introduction

When a product is designed, the requirements on the size, shape and mass properties of the product might need to be fulfilled. For example, the centre of gravity of a rotational part (e.g. a cam) may be required to be at a preset location. If its mass properties cannot meet some of the requirements (e.g. the location of its centre of gravity), the user may need to change the design. This is not always possible if any change in the shape or size of the product is not allowed. In this paper, one of the mass properties—the centre of gravity is taken into consideration and a method is provided for altering the centre of gravity of a model. In this method, to achieve the target of changing the centre of gravity of a model without violating its shape, either materials of different density could be added into the interior of the model or the model could be hollowed out. In the former case, a multiple material object is created. In the latter case, a hollowed prototype is formed. To produce these objects, the process employed for making them must be capable of fabricating multiple material or hollowed objects.

Rapid Prototyping (RP) technologies include those processes that can produce multiple material prototypes and hollowed prototypes [1], [2], [3], [4], [5]. When a multiple material model is created, it must be represented and different representation schemes can be found in [6], [7]. RP technologies are also very useful in making prototypes for visual check and functional test purposes in a product development cycle. Using RP technologies, a prototype can be fabricated in a shorter time as compared to the traditional manufacturing technologies and the lead-time in a product development cycle can be reduced.

To further speed up the process of making prototypes, in Refs. [8], [9], [10], instead of solid prototypes, hollowed prototypes are built by the RP processes so that shorter build time and less material [11] would be required for the fabrication process. This is an advantage as the cost of fabricating a prototype would be reduced. However, when a solid is hollowed out, there is no consideration on the location of its centre of gravity and in most of the cases, the centre of gravity of the hollowed model is different from that of its solid counterpart. This is acceptable if the fabricated prototype is used for the purpose of visual check. However, for functional test purpose, dynamical balancing problems may arise and unexpected situations may occur. Also, the actual property of a product might not be reflected from the functional test. As a result, a hollowed prototype could not be used for functional test purposes and the advantage of building a hollowed prototype could not be achieved.

In this paper, a method is established for controlling the location of the centre of gravity of a model. This method could be used in two cases: the first is to maintain the centre location of a hollowed model, and the second is to change the centre location of a solid by hollowing. In the first step of the method, a hollowed portion is formed from a solid model by applying the hollowing algorithm described in [10]. Then an algorithm is proposed for changing the location of the centre of gravity of a hollowed portion. Using this algorithm, the two cases stated above can be achieved by:

  • 1.

    keeping the centre of gravity of a hollowed portion to be at that of its solid so that the centre location of a hollowed model can be maintained; and

  • 2.

    shifting the centre of gravity of a hollowed portion to a desired location so that the centre of gravity of the solid is changed when it is hollowed out by the hollowed portion.

In Section 2, the hollowing algorithm is reviewed. The algorithm for controlling the centre of gravity of a hollowed portion is described in Section 3. The implementation of the algorithm on an example model is given in Section 4 and a discussion of the method is presented in Section 5.

Section snippets

Hollowing algorithm

In Ref. [10], an algorithm for hollowing out a solid model was proposed. In this algorithm, the hollowed portion of a solid is formed from voxels. To create a proper hollowed model such that the original boundary of a solid would not be violated (Fig. 1), the voxels must be completely inside the solid. Also, the minimum distance between the surfaces of the voxels and the solid must be equal to a preset value t, so that a hollowed model does not contain any zero thickness location on its

Algorithm for moving the centre of gravity of a hollowed portion

In this section, an algorithm is proposed such that when a hollowed portion is formed from a solid model, its centre of gravity could be moved to a desired location. The algorithm consists of two steps. First, the centre of gravity (CG) of the hollowed portion is moved to an arbitrary axis passing through the desired location. In the second step, the CG is subsequently shifted to the desired location. When the purpose of applying the algorithm is to maintain the location of the centre of

Implementation

The cam shown in Fig. 25 is used as an example to illustrate the application of the algorithm for controlling the centre location of a hollowed model. In this example, the centre of the hollowed cam must be the same as the original solid. The volumes and the centre locations of the solid, its hollowed portion and the hollowed model are given in Table 3. In this example, the direction of the specified axis is set as (1, 0, 0) and the desired location is the centre location of the solid. According

Discussion

In this paper, an algorithm is proposed for controlling the centre of gravity of a hollowed portion which is built up by voxel elements and it provides an automatic method for adjusting the location of the centre of gravity of a model. In this algorithm, two types of movements—A and B are introduced. To move the centre of gravity to a specified axis, type A movement is required. To move it to a specified location, both movements are needed and type B movement can be applied only if type A

Acknowledgements

The authors would like to thank The University of Hong Kong and the Research Grant Council of The HKSAR Government for providing financial support to W.K. Chiu.

References (12)

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