Research Papers

Geometric Error Effects on Manipulators' Positioning Precision: A General Analysis and Evaluation Method

[+] Author and Article Information
Henrique Simas

Raul Guenther Laboratory of Applied Robotics,
Department of Mechanical Engineering,
Federal University of Santa Catarina,
Florianópolis, SC 88040-900, Brazil
e-mail: henrique.simas@ufsc.br

Raffaele Di Gregorio

Department of Engineering,
University of Ferrara,
Via Saragat, 1,
Ferrara 44100, Italy
e-mail: rdigregorio@ing.unife.it

1Corresponding author.

Manuscript received February 28, 2016; final manuscript received August 15, 2016; published online October 6, 2016. Assoc. Editor: Leila Notash.

J. Mechanisms Robotics 8(6), 061016 (Oct 06, 2016) (10 pages) Paper No: JMR-16-1049; doi: 10.1115/1.4034577 History: Received February 28, 2016; Revised August 15, 2016

Manufacturing and assembly (geometric) errors affect the positioning precision of manipulators. In six degrees-of-freedom (6DOF) manipulators, geometric error effects can be compensated through suitable calibration procedures. This, in general, is not possible in lower-mobility manipulators. Thus, methods that evaluate such effects must be implemented at the design stage to determine both which workspace region is less affected by these errors and which dimensional tolerances must be assigned to match given positioning-precision requirements. In the literature, such evaluations are mainly tailored on particular architectures, and the proposed techniques are difficult to extend. Here, a general discussion on how to take into account geometric error effects is presented together with a general method to solve this design problem. The proposed method can be applied to any nonoverconstrained architecture. Eventually, as a case study, the method is applied to the analysis of the geometric error effects of the translational parallel manipulator (TPM) Triflex-II.

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Grahic Jump Location
Fig. 1

Graph of a manipulator with general architecture: Vertices and arcs represent links and joints, respectively; Li for i = 1,…,n are the open kinematic chains (legs) that simultaneously connect the platform to the base, whereas Lt is an added virtual kinematic chain

Grahic Jump Location
Fig. 2

Triflex-II: (a) kinematic scheme and (b) platform's reference points

Grahic Jump Location
Fig. 3

Introduction of the geometric errors: (a) PRRU and (b) PRRR legs with geometric errors

Grahic Jump Location
Fig. 4

Workspace boundaries: (a) intersection with the xbyb-plane, (b) intersection with the ybzb-plane, (c) intersection with the xbzb-plane, and (d) 3D view (the grayscale indicates the zb value in length unit)

Grahic Jump Location
Fig. 5

Values of δg,R when Op lies on the boundary surface of the workspace (a), on the plane z = 0 (b), and on the planes z = ±0.75 l.u. (c) for θ3∈[0, π] and θ7∈[0, π] (the curves are the contour lines, and the grayscales indicate the δg,R value)

Grahic Jump Location
Fig. 6

Values of εg,R when Op lies on the boundary surface of the workspace (a), on the plane z = 0 (b), and on the planes z = ±0.75 l.u. (c) for θ3∈[0, π] and θ7∈[0, π] (the curves are the contour lines, and the grayscales indicate the εg,R value in length unit per radians])



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