Friction stir welding (FSW) has been widely applied in a number of fields instead of traditional fusion welding. However, a huge axial downward force is required to maintain a steady welding process. Moreover, the task of welding along a curved surface requires an orientation ability, which traditional FSW machines cannot provide. To overcome this limitation, we propose a 5-axis hybrid robot for FSW. This hybrid robot comprises a 2-SPR-RPS parallel mechanism (with one translational degree of freedom and two rotational degrees of freedom) and two gantries. First, mobility of the parallel mechanism in the initial and general configuration is analyzed using screw theory and continuous rotational axes are identified. Second, forward and inverse position solutions to the hybrid robot are studied, and the Jacobian matrix of the parallel mechanism is obtained. By analyzing the motion/force transmissibility, the architectural parameters of the parallel mechanism are optimized. Finally, the reachable workspace of the end effector is obtained considering the constraints of actuation links, joint angles, and singular configuration.

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Mobility is a basic property of a mechanism. The aim of mobility analysis is to determine the number of degrees-of-freedom (DOF) and the motion pattern of a mechanism. The existing methods for mobility analysis have some drawbacks when being applied to limited-DOF parallel mechanisms (PMs). Particularly, it is difficult to obtain a symbolic or closed-form expression of mobility and its geometric interpretations are not always straightforward. This paper presents a general method for mobility analysis of limited-DOF PMs in the framework of geometric algebra. The motion space and constraint space of each limb are expressed using geometric algebra. Then the mobility of the PM can be calculated based on the orthogonal complement relationship between the motion space and the constraint space. The detailed mobility analyses of a 3-RPS PM and a 3-RPC PM are presented. It is shown that this method can obtain a symbolic expression of mobility with straightforward geometric interpretations and is applicable to limited-DOF PMs with or without redundant constraints. Without solving complicated symbolic linear equations, this method also has computational advantages.