## 1 Introduction
Other examples of using local closed-loop linkages to optimize the design and control for a robot can be found in [26; 27; 28; 29; 30; 31; 32; 33; 34]. In recent decades, a huge number of hybrid robot prototypes and products have been designed and developed [10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30]. The dynamic modelling and control for some of these complex robots have been addressed as well. However, to develop a generic method for formulating the dynamic model of a generalized hybrid robot mechanism is challenging. In the literature, there have been efforts that focused on the kinematic modelling of the hybrid robots Class I [1; 2; 3; 4; 5]. The kinematic modelling and analysis of two serially connected parallel mechanisms were investigated in [1]. In [2], the kinematic redundancy issue of a serial-parallel manipulator was addressed. The Screw theory and the Jacobian approach were applied for the kinematic modelling of a serial-parallel robot [34]. In particular, the dynamics and the structural stiffness models of some specific hybrid robots Class I were formulated and analysed [6; 7; 8; 9]. There have also been attempts working on the modelling and analysis of the hybrid robots Class II [11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21]. A real-time implementation of path planning, trajectory generation, and servo control for a hybrid manipulation was presented in [11]. The kinematic modelling, the kinematic design, the workspace modelling and other aspects related to the kinematics of the hybrid robots Class II were studied [12; 13; 14; 15; 16; 17]. The dynamic modelling and analysis of the robots Class II were also investigated [18; 19]. In addition, the structural synthesis and the stiffness of the hybrid robots of this class were studied [20; 21; 22]. Apart from the aforementioned works, there have been investigations that emphasized on design and development of the hybrid robots Class III [25; 26; 27; 28; 29; 30; 31; 32; 33]. A valuable comparison of the conventional serial robot architectures and the hybrid robots Class III was presented in [34]. In the research [25], some theoretical issues related to the kinematic modelling of multi closed-loop mechanisms were addressed. In addition, some closed-form solutions to the kinematics problem of individual hybrid robots Class III were presented in [26; 27; 28]. These solutions played an important role in validating the design of the robots. The workspace and mobility analysis were also investigated in [28; 29]. Other aspects related to the design analysis of heavy-duty robots were presented in [30; 31]. The control issues were studied in [32; 33]. It is noticeable that the dynamic modelling of a hybrid manipulator Class III (forestry robot) was investigated in [33]. However, the effects of the local closed-loops on the dynamic responses of this robotic system were overlooked. Most of the efforts working on the hybrid robots Class III mainly focused on the design and control of some individual robots for the kinematical aspects. Though the dynamic modelling of the robots was addressed in a few researches, e.g., [33], however, the mass and inertia of the local closed-loop linkages that have significant effects on the robot motion were neglected; the geometrical and kinematical constraints due to the presence of the local closed-loop linkages were usually ignored. Moreover, little attention has been paid to the development of a general method for the kinematic and dynamic modelling of this robot class. Therefore, in this paper, a new method for designing the kinematic chain and formulating the dynamic model of the hybrid robots is developed. First, a generic scheme for the kinematic design of a generalized hybrid robot mechanism is proposed. In this scheme, the generalized hybrid mechanism is synthesized with m local closed-loop linkages appended to a general n-link serial manipulator.