LINAPOD — Machine Tools as Parallel Link Systems Based on a Modular Design

Wurst, Karl-Heinz

doi:10.1007/978-1-4471-0885-6_27

Cited by 19 publications

(4 citation statements)

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“…Let Da i = Dl 0 (i = 1, 2), Da i = Ds 0 + Db 0 , i = 3 be the comprehensive error vector of the origin of A i referenced to O 0 g ; c 3 = u B i + u C i À u A i be the orientation error of O 0 g referenced to O g ; Dg i = À2(Dc i À Da i ) the relative joint distance error on both sides of the parallelogram and take the product of w T i on both sides of equations (12) - (14). Then, we have…”

Section: Error-mapping Modelmentioning

confidence: 99%

“…the relative joint distance error on both sides of the parallelogram and take the product of w T i on both sides of equations ( 12) - (14). Then, we have…”

Section: Error-mapping Modelmentioning

confidence: 99%

“…Although the above approaches are widely used for error models, they cannot separate compensatable and uncompensatable error sources. As the pose error of lower-mobility parallel manipulators cannot be compensated, 14 these approaches are not suitable for such manipulators. Bearing this in mind, Huang et al, 15 taking a 3-DOF parallel kinematic machine with parallelogram struts as an example, proposed a modeling method to separate the geometric error sources which affect the position and orientation errors in the end-effector.…”

Section: Introductionmentioning

confidence: 99%

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Error modeling and tolerance design of a parallel manipulator with full-circle rotation

Shao

Zhang

et al. 2016

Advances in Mechanical Engineering

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A method for improving the accuracy of a parallel manipulator with full-circle rotation is systematically investigated in this work via kinematic analysis, error modeling, sensitivity analysis, and tolerance allocation. First, a kinematic analysis of the mechanism is made using the space vector chain method. Using the results as a basis, an error model is formulated considering the main error sources. Position and orientation error-mapping models are established by mathematical transformation of the parallelogram structure characteristics. Second, a sensitivity analysis is performed on the geometric error sources. A global sensitivity evaluation index is proposed to evaluate the contribution of the geometric errors to the accuracy of the end-effector. The analysis results provide a theoretical basis for the allocation of tolerances to the parts of the mechanical design. Finally, based on the results of the sensitivity analysis, the design of the tolerances can be solved as a nonlinearly constrained optimization problem. A genetic algorithm is applied to carry out the allocation of the manufacturing tolerances of the parts. Accordingly, the tolerance ranges for nine kinds of geometrical error sources are obtained. The achievements made in this work can also be applied to other similar parallel mechanisms with full-circle rotation to improve error modeling and design accuracy.

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Section: Error-mapping Modelmentioning

confidence: 99%

“…the relative joint distance error on both sides of the parallelogram and take the product of w T i on both sides of equations ( 12) - (14). Then, we have…”

Section: Error-mapping Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Error modeling and tolerance design of a parallel manipulator with full-circle rotation

Shao

Zhang

et al. 2016

Advances in Mechanical Engineering

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“…This example considers the six-dof parallel kinematic machine tool Linapod (Pritschow et al 2004;Wurst, 1998) installed at the Institute for Control Engineering of Machine Tools and Manufacturing Units at the University Stuttgart (Germany), see Fig. 8.…”

Section: Error Analysis For a Parallel Kinematic Manipulatormentioning

confidence: 99%

Kinematic Modeling, Linearization and First-Order Error Analysis

Pott¹,

Hiller²

2008

Parallel Manipulators, Towards New Applications

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Robot Kinematics

Zhang¹,

Bi²,

Gao³

2008

Wiley Encyclopedia of Computer Science and Engineering

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In this article, kinematics of robot manipulators is presented with a systematic and general approach—Denavit‐Hartenberg convention. The basic mathematical concepts are explained in detail, including translational transformation, rotational transformation, homogeneous transformation, Euler angle, direct kinematics and inverse kinematics, and so on. The relation between joint velocities and end‐effector linear and angular velocities is described by the Jacobian matrix. As an example, a parallel manipulator with three degrees of freedom (DOFs) is presented. This 3DOF‐parallel manipulator can be used for machine tools, and it includes two rotations and one translation along the z axis. Both direct and inverse kinematic problems are conducted based on the theory described in the beginning of the article. The case study will allow readers to better understand the knowledge of robot kinematics.

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LINAPOD — Machine Tools as Parallel Link Systems Based on a Modular Design

Cited by 19 publications

References 1 publication

Error modeling and tolerance design of a parallel manipulator with full-circle rotation

Error modeling and tolerance design of a parallel manipulator with full-circle rotation

Kinematic Modeling, Linearization and First-Order Error Analysis

Robot Kinematics

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