This paper presents a parametric stiffness analysis of the Orthoglide, a 3-DOF translational Parallel Kinematic Machine. First, a compliant modeling of the Orthoglide is conducted based on an existing method. Then stiffness matrix is symbolically computed. This allows one to easily study the influence of the geometric design parameters on the matrix elements. Critical links are displayed. Cutting forces are then modeled so that static displacements of the Orthoglide tool during slot milling are symbolically computed. Influence of the geometric design parameters on the static displacements is checked as well. Other machining operations can be modeled. This parametric stiffness analysis can be applied to any parallel manipulator for which stiffness is a critical issue.
This paper addresses an interval analysis based study that is applied to the design and the comparison of 3-DOF parallel kinematic machines. Two design criteria are used, (i) a regular workspace shape and, (ii) a kinetostatic performance index that needs to be as homogeneous as possible throughout the workspace. The interval analysis based method takes these two criteria into account: on the basis of prescribed kinetostatic performances, the workspace is analysed to find out the largest regular dextrous workspace enclosed in the Cartesian workspace.An algorithm describing this method is introduced. Two 3-DOF translational parallel mechanisms designed for machining applications are compared using this method. The first machine features three fixed linear joints which are mounted orthogonally and the second one features three linear joints which are mounted in parallel.In both cases, the mobile platform moves in the Cartesian x − y − z space with fixed orientation.
Parallel Kinematic Mechanisms (PKM) are interesting alternative designs for machine tools. A design method based on velocity amplification factors analysis is presented in this paper. The comparative study of two simple two-degree-of-freedom PKM dedicated to machining applications is led through this method: the common desired properties are the largest square Cartesian workspace for given kinetostatic performances. The orientation and position of the Cartesian workspace are chosen to avoid singularities and to produce the best ratio between Cartesian workspace size and mechanism size. The machine size of each resulting design is used as a comparative criterion.
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