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Technical Briefs

# Error Analysis of a 3-DOF Parallel Mechanism for Milling Applications

[+] Author and Article Information
G. E. E. Gojtan

UNINOVE - Associação
Educacional Nove de Julho,
Sao Paulo 01005-010, Brazil

T. A. Hess-Coelho

e-mail: tarchess@.usp.br
Department of Mechatronics and Mechanical Systems Engineering,
University of Sao Paulo,
Sao Paulo 01005-010, Brazil

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 17, 2010; final manuscript received January 30, 2013; published online June 10, 2013. Assoc. Editor: Vijay Kumar.

J. Mechanisms Robotics 5(3), 034501 (Jun 24, 2013) (9 pages) Paper No: JMR-10-1178; doi: 10.1115/1.4024235 History: Received December 17, 2010; Revised January 30, 2013

## Abstract

Parallel mechanisms have been investigated during the last two decades, due to the fact that they present some advantages in a comparison with serial structures. This work deals with the error analysis of a 3-dof asymmetric parallel mechanism, purposely conceived for milling applications. In a comparison with the previous proposed concepts, this type of kinematic structure demonstrates a promising behavior. Topologically, the architecture is simpler and lighter than Tricept because it has no central passive limb. In addition, only the constraining active limb needs to satisfy the parallelism and orthogonality conditions. Furthermore, one degree of freedom, associated to the third actuator, is decoupled from the other two. Important issues, related to this type of kinematic structure, such as the mappings of the tool positioning error throughout the available workspace, due to the actuators imprecisions and manufacturing tolerances, are discussed in detail.

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## Figures

Fig. 1

Structural synthesis: (a) the constraining limb and (b) the CAD model of the 2 UPS + PRP

Fig. 2

The notation for the position analysis

Fig. 3

An example of singular configuration when det JP is null: points U1, U2, S1, and S2 belong to the same plane

Fig. 4

First mapping of the kinematic error in the x-direction, assuming that Δh1 = Δh2 = Δh3 = 5 μm, for (a) H = 240 mm and (b) H = 480 mm

Fig. 5

First mapping of the kinematic error in the y-direction, assuming that Δh1 = Δh2 = Δh3 = 5 μm, for (a) H = 240 mm and (b) H = 480 mm

Fig. 6

Second mapping of the kinematic error in the x-direction, assuming that Δh1 = Δh3 = 5 μm and Δh2 = −5 μm, for (a) H = 240 mm and (b) H = 480 mm

Fig. 7

Second mapping of the kinematic error in the y-direction, assuming that Δh1 = Δh3 = 5 μm and Δh2 = −5 μm, for (a) H = 240 mm (b) H = 480 mm

Fig. 8

First mapping of the geometric error in the x-direction, assuming the symmetrical condition, for (a) H = 240 mm and (b) H = 480 mm

Fig. 9

First mapping of the geometric error in the y-direction, assuming the symmetrical condition, for (a) H = 240 mm and (b) H = 480 mm

Fig. 10

Second mapping of the geometric error in the x-direction, assuming the asymmetric condition, for (a) H = 240 mm and (b) H = 480 mm

Fig. 11

Second mapping of the geometric error in the y-direction, assuming the asymmetric condition, for (a) H = 240 mm and (b) H = 480 mm

Fig. 12

Sensitivity of variable θ with respect to the 12 parameters, for (a) H = 240 mm and (b) H = 480 mm

Fig. 13

Sensitivity of variable R with respect to the 12 parameters, for (a) H = 240 mm and (b) H = 480 mm

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