• Journal of the Korean Society for Precision Engineering
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• v.16 no.5 s.98
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• pp.200-208
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• 1999

The statics relation of the Stewart platform has been investigated from the viewpoint of the forward and inverse force transmission analyses. Two eigenvalue problems corresponding to the forward and inverse force transmission analyses have been formulated. The forward force transmission analysis is to determine the ranges of the magnitudes of the force and moment generated at the end-effector for the given magnitude of linear actuator forces. In reverse order, the inverse force transmission analysis is to find the range of the magnitude of actuator forces for the given ranges of the magnitudes of the force and moment at the end-effector. The inverse force transmission analysis is important since it can provide a designer with a valuable information about how to choose the linear actuators. It has been proved that two eigenvalue problems have a reciprocal relation, which implies that solving either of the eigenvalue problems may complete the forward/inverse force transmission analysis. A numerical example has been also presented.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.4
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• pp.109-121
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• 1996

This paper presents how the input forces along the prismatic joints of a parallel manipulator are transmitted to the upper platform. In order to consider force transmission and moment transmission seperately the Jacobian matrix for parallel manipulators is splitted into two parts. Magnitudes of input forces on the six actuators at a given manipulator configuration which generate maximum/minimum output force with no moment generated on the platform are obtained through the singular value decomposition of a matrix involving the Jacobian. Similarly the directions of the input forces to obtain only the rotation of the platform have been analyzed. Using the singular values a simple equation for the volume of ellipsoid which is a good tool for manipulability measure is provided. Obtained results could be useful in determinimg design parameters like radius of plaform, angles between joints, etc. Simulations are porvided.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.11
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• pp.213-223
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• 1999

In this paper, input-output transmission characteristics of the Eclipse, which is a parallel machine tool capable of 5 face rapid machining, are investigated. By splitting the weighted Jacobian matrix into two parts, the force and moment transmission characteristics together with the velocity and angular velocity transmission characteristics are analyzed. A new manipulability measure, which combines the volume of the manipulability ellipsoid and the condition number of the splitted Jcobian matrix, is proposed. Two link parameters, the ratio of upper and lower platforms' radii and the length of a supporting link of the Eclipse, are designed by applying the new manipulability measure derived. Computer simulations are provided.