【正文】 indicates that the object can rotate about the yaxis.Observing only leg 1, the capability of the endeffector in the leg can be expressed as . Letting leg 1 alone, the capability of the endeffector with leg 2 can be written as Then, the intersection of and is ， i. e, (1)which describes the capability of the robot, ., the translations of the endeffector along the x and y axes. This means the endeffector has two purely translational degrees of freedom with respect to the base.It is noteworthy that the capability analysis method used above cannot be applied to all parallel robots.2 Kinematics analysis Inverse kinematicsAs illustrated in Fig. 1(b), a reference frame :Oxy is fixed to the base at the joint point and a moving reference frame ： is attached to the endeffector, where is the reference point on the endeffector. Vectors are defined as the position vectors of points in the frame ，and vectors as the position vectors of points in frame .The geometric parameters of the robot are ，and the distance from point to the guideway is ,where and and are dimensional parameters, and and nondimensional parameters. The position of point in the fixed frame is denoted as vector (2)The vectors of in the fixed frame can be written as (3)where is the actuated input for leg 1. Vector in the fixed frame can be written as (4)The inverse kinematics problem of leg 1 can be solved by writing the following constraint equation (5)that is (6)Then, there is (7)where (8)For leg 2，it is obvious thats = x (9)in which s is the input of leg 2. From Eqs. (8) and (9), we can see that there are two solutions for the inverse kinematics of the robot. Hence, for a given robot and for prescribed values of the position of the endeffector, the required actuated inputs can be directly puted from Eqs. (7) and (9). To obtain the configuration as shown in Fig. 1, parameter a in Eq. (8) should be 1. This configuration is called the “ + ” working mode. When , the corresponding configuration is referred to as the “一” working mode. Forward kinematicsThe forward kinematic problem is to obtain the output with respect to a set of given inputs. From Eqs. (6) and (9),one obtains (11)andx = s (12)where and . Therefore , there are also two forward kinematic solutions for the robot. The parameter corresponds to the configuration shown in Fig. 1, which is denoted as the downconfiguration. When the configuration is referred to as the upconfiguration. These two kinds of configurations correspond to two kinds of assembly modes of the robot.3 Singularity analysis4 Workspace analysis5 Conclusion and future workIn this paper , a novel 2DOF translational robot is proposed. One characteristic of the robot is that it can position a rigid body in a 2D plane while maintaining a constant orientation. The proposed robot has potential application in light indus。在這里首先要感謝我的導(dǎo)師………………附錄（一） 英文文獻(xiàn)Structure and kinematic analysis of a novel 2DOF translational parallel robotChen Tao1．Wu Chao2 and Liu xiujun2**( 1. School of Application Science and Technology．Harbin University of ScienceAnd Technology，Harbin l50080,China；2. Department of Precision Instruments．Tsinghua University, Beijing 100084, China)Accepted on February 13, 2007Abstract This paper addresses the analysis of a novel parallel robot with 2 translational degrees of freedom (DOFs). The robot can position a rigid body in a plane with constant orientation. The kinematic structure of the robot is first described in detail, Some kinematic problems, such as the inverse and forward kinematics, velocity, and singularity are then analyzed. The working and assembly modes are discussed. Since it is the most important index to design a robot , the workspace of the robot is studied systematically in this paper. Based on the analysis of reachable workspace and singularity, a kind of workspace concept characterizing the region that the endeffector of the robot can reach in practice is defined. The results of this paper will be very useful for the design and application of the robot.Keywords： parallel robot, degree of freedom, kinematics workspace. The conceptual design of parallel robots can be dated back to the time when Gough established the basic principles of a device with a closedloop kinematic structure that can generate specified position and orientation of a moving platform so as to test tire wear and. tear. Based on this principle, Stewart designed a platform used as an aircraft simulator in 1965. In 1978, Hunt made a systematic study of robots with parallel kinematics, in which the spatial 3RPS (Rrevolute joint，Pprismatic joint, and S spherical joint) parallel robot is a typical one. Since then, parallel robots have been studied extensively by numerous researchers.The parallel robots with 6 DOFs possess the advantages of high stiffness, low inertia, and large payload capacity. However, they suffer the problems of relatively small useful workspace and design difficulties .Their direct kinematics possess a very difficult problem. The same problem of parallel robots with 2 and 3 DOFs can be described in a closed form . As is well known, there are three kinds of singularities in parallel robots. Generally, not all singularities of a 6 DOF parallel robot can be found easily. For a parallel robot with 2 or 3 DOFs, the singularities can always be identified readily. For such reasons, parallel robots with less than 6 DOFs, especially 2 and 3 DOFs, have increasingly attracted more and more researchers attention with respect to industrial applications. In these designs, parallel robots with three translational CKDFs have been playing important roles in the industrial applications. For example, the design of the DELTA robot is covered by a family of 36 patents. Tsai’s robot，in which each of the three legs consists of a parallelogram, is