The moving platform of an RPR-equivalent parallel mechanism (PM) can undergo a 3-degree-of-freedom (DOF) motion that is the product of a rotation followed by a translation and another rotation. A 5-DOF hybrid parallel manipulator can be developed by adding an x-y gantry or an RR serial mechanism to an RPR-equivalent PM, which is suitable for manipulations requiring high rigidity and accuracy with good dexterity along surfaces of the 3-D space. This paper investigates the type synthesis of the RPR-equivalent PM. First, the RPR motion is briefly discussed. Then, the kinematic bonds of limb chains and their mechanical generators are presented. Structural conditions for constructing an RPR-equivalent PM are presented. Furthermore, the RPR-equivalent PMs are classified into several categories, depending on the DOF of its limb chains. Numerous new architectures of the RPR-equivalent PMs are synthesized.

Parasitic motion is a major drawback of the general 1T2R parallel mechanism (PM), where T denotes a translation degree of freedom (DOF) and R a rotational DOF. This paper investigates the type synthesis of the 1T2R PM without parasitic motion. First, a brief review on the planar–spherical bond and its mechanical generators is presented. Then, the difference between the general and special$a$T$b$R motion is discussed. Relations between the parasitic motion and the general and special$a$T$b$R motion are revealed. An infinitesimal 1T2R PM with rotation bifurcation is presented as a special case. Further, the definition of the 1T2R PM without parasitic motion is presented, and the limb bond {${\bf G}$(${\bf u}$)}{${\bf S}$($N$)} is identified. Geometrical conditions to construct an 1T2R PM without parasitic motion are presented, and nonoverconstrained 1T2R PMs without parasitic motion are synthesized. Idle pairs in the nonoverconstrained 1T2R PMs without parasitic motion are detected. Finally, overconstrained 1T2R PMs without parasitic motion are obtained by removing the idle pairs in the nonoverconstrained 1T2R PMs.

One important category of parallel mechanisms is the translational parallel mechanism (TPM). This paper focuses on the structural shakiness of the non overconstrained TPM. Such a structural shakiness is due to the unavoidable lack of rigidity of the real bodies, which leads to uncheckable orientation changes of the moving platform of a TPM. Using algebraic properties of displacement subsets and, especially, displacement Lie subgroup theory, we show that the structural shakiness of the non overconstrained TPM is inherently determined by the structural type of its limb chains. A structural shakiness index (SSI) for a non overconstrained TPM is introduced. When the set of feasible displacements of the end body of a 5-degree-of-freedom (DOFs) limb chain contains two infinities of parallel axes of rotation, we have SSI = 2; when the displacement set of the end body of a 5-DOF limb chain contains only one infinity of parallel axes of rotation, we have SSI = 1. It is proven that non over con stained TPMs constructed with limb chains with SSI = 1 are much less prone to orientation changes than those constructed with limb chains with SSI = 2. Based on the SSI, we enumerate limb kinematic chains and construct 21 non overconstrained TPMs with less shakiness.

Type synthesis of lower mobility parallel mechanisms (PMs) has attracted extensive attention in research community of robotics over the last seven years. One important trend in this area is to synthesize PMs with prespecified motion properties. This paper focuses on the type synthesis of a special family of PMs whose moving platform can undergo a bifurcation of Schoenflies motion. First, bifurcation of Schoenflies motion in PMs is interpreted in terms of displacement group theory and the basic limb bond {X(y)}{R(N,x)} is identified. Further, the geometric condition for constructing a PM with bifurcation of Schoenflies motion is presented. The kinematic equivalence between {X(y)}{R(N,x)} and {X(y)}{X(x)} is proven. Four subcategories of irreducible representation of the product {X(y)}{X(x)} are proposed and the limb chains that produce the desired limb bond are synthesized. Finally, the partitioned mobility of PMs with bifurcation of Schoenflies motion and its effect on actuation selection are discussed.

The paper describes some details of the mechanical and kinematics design of a five-axis mechanism. The design has been utilized to physically realize an industrial-scale five-axis milling machine that can carry a three KW spindle. However, the mechanism could be utilized in other material processing and factory automation applications. The mechanism has five rectilinear joints/axes. Two of these axes are arranged traditionally, i.e. in series, and the other three axes utilize the concept of parallel kinematics. This combination results in a design that allows three translational and two rotational two-mode degrees of freedom (DOFs). The design provides speed, accuracy and cost advantages over traditional five-axis machines. All axes are actuated using linear motors.

Using algebraic properties of displacement (or rigid-body motion) subsets, the paper introduces new two-degree-of-freedom (2-DOF) nonoverconstrained orientation mechanisms. The angles of pan and tilt are also referred to as the angles of precession /spl psi/ and nutation /spl theta/, respectively, employing the standard terminology of Euler angles. A serial array of two revolute pairs provides the kinematic constraint of an end-effector. For instance, the first axis of rotation is fixed vertically, and the second axis rotates around the first axis, remaining parallel to the horizontal plane. Such a 2-DOF wrist is fit for orienting various devices like telescopes, cameras, antennas, etc. The first axis is fixed, and can be actuated by any powerful heavy servomotor. The paper discloses new mechanisms that allow the actuation of the second movable axis by a fixed servomotor. Moreover, the actuation of the movable axis is not a function of the pan /spl psi/. In other words, the pan and the tilt are controlled independently or in a fully uncoupled manner.

The use of lower mobility parallel manipulators with less than six degrees of freedom (DOFs) has drawn a lot of interest in the area of parallel robots. In this paper, the type synthesis of 3R2T 5-DOF parallel mechanisms (PMs) is performed systematically using the Lie group of displacements, where R denotes a rotational DOF, and T denotes a translational DOF. First, some necessary theoretical fundamentals about the displacement group are recalled. Then, a general approach is proposed for the type synthesis of 3R2T 5-DOF PMs. The limb kinematic chains, which produce the desired displacement manifolds, are synthesized and enumerated. Structural conditions, which guarantee that the intersection of the displacement manifolds generated by the limb is the desired 5-DOF manifold, are presented. An exhaustive enumeration of 3R2T 5-DOF symmetrical PMs is obtained. Finally, an input selection method is proposed.

A 3 DOF micro finger, that has pure translational motion, is proposed. The finger will be applied in the two finger micro manipulation in order to manipulate micrometer size objects dexterously. The possible configurations are considered based on the group theory. Then, the optimal configuration is proposed by taking simple machining of joint structures into account. Kinematics analysis is made in order to describe the relation between end effector and actuator displacements. The design parameters are examined by evaluating the force capability of the actuator and the work space volume. Basic experiments are made by a prototype finger module that show excellent micro motion capability.