Abstract—This paper presents synthesis methods and performance measures for wire-actuated wrists using a universal-joint constraining linkage. Performance measures based on the isotropy of the wrench-closure workspace are derived and used in generating design atlases as a function of non-dimensional design parameters. The performance indices that are optimized include wrench-closure workspace, isotropy of the wrench-closure workspace, and kinematic conditioning index. Stiffness is used to define a safety margin from singularities of wrench closure. A design example of a wire- actuated surgical wrist is presented and validated through simulation. The methods presented in this paper are useful for quick dimensional synthesis of wire-actuated wrists with predefined wrench-closure workspaces. I. INTRODUCTION N many applications of minimally-invasive or non- invasive surgery, increased miniaturization of surgical wrists is essential to successfully performing surgeries in restricted areas. Miniaturization permits increases in distal- end dexterity as required for some surgeries. Another advantage of miniaturization is the increase in the number of surgical wrists and tools that can be employed without increasing the number or size of access incisions. Previous papers have proposed the use of wire-actuated mechanisms in surgical applications. One of the major advantages of wire-actuation in these applications is light weight and small size [1]. It has also been proposed for high lateral flexibility, which allows transmission of force to hard-to-reach locations and through tight bending radii [2][3]. Because surgical applications such as suturing often require rotation about the output axis of the wrist, it is necessary to include a constraining linkage which eliminates unwanted degrees of freedom and allows torque transmission along the wrist. Flexible, continuous-backbone designs of wire-actuated wrists have been presented by [4], [5], and others. A number of articulated designs are also evident in the literature, which use rigid central linkages that are capable of transmitting torque (e.g. [8], [9]). In [10] an articulated design was presented that uses multiple universal Manuscript received September 15, 2008. Saleem Abdul Hamid (e-mail: sh2581@columbia.edu) and Nabil Simaan (212-854-2957, e-mail: ns2236@columbia.edu) are with the department of Mechanical Engineering, Columbia University, New York, NY 10027. Saleem Abdul Hamid was supported from National Science Foundation (NSF) under Engineering Research Center grant #EEC9731478 and by Columbia University internal funds.  Corresponding author joints in a parallel configuration. Using a universal-joint as the constraining linkage enables transmission of high torques at many tilt angles (unlike other rigid central linkages) while providing very good lateral stiffness (unlike flexible, continuous designs). Unfortunately, the universal joint also has a number of disadvantages that designers must be aware of. The uneven transmission of torque [11] and the singularities associated with some configurations at extreme tilt angles are the most important of these disadvantages and will be explored through wrench-closure workspace analysis in this paper. In addition, the limitations of wire-actuation and the problems associated with wire stiffness are addressed through the formulation of design atlases and safety margins from workspace boundaries. The goal of this paper is to offer an easy reference for designers of wire-actuated, universal-joint wrists to optimize designs for desired performance. The analyses performed apply generally to universal-joint wrists actuated by three wires. Because of this, the physical feasibility of the mechanical design is not completely resolved in this paper. It will be required of the individual designer to determine if it is possible to actually manufacture a design with the optimal parameters given and, if not, iterate to a workable design that also has the required performance. Also, since the design optimization is based on purely kinematic considerations, this approach to design may not be suitable for certain cases, especially miniature wrists, in which stiffness, friction, and limited tolerances play a critical role early in the design process. Fig. 1. Example of a specific wire-actuated universal-joint wrist design with the parameters used for analyzing generic wrists. The figure on the right shows bending angle,  and plane angle,  . Fig. 1 shows an example design and some of the relevant dimensions of a general universal-joint wrist. The two dimensionless parameters that will be optimized for the various performance indices are the height over the top diameter, ß, and the base diameter over the top diameter, ø. The height for a general universal joint is defined as the Design and Synthesis of Wire-Actuated Universal-Joint Wrists for Surgical Applications Saleem Abdul Hamid, Nabil Simaan  I  Height D_bottom D_top  2009 IEEE International Conference on Robotics and Automation Kobe International Conference Center Kobe, Japan, May 12-17, 2009 978-1-4244-2789-5/09/$25.00 ©2009 IEEE 1807