This paper presents a closed-form solution to the four-position synthesisproblem by using a spatial slider, which is a spatial dyad of two perpendicularlyintersected cylindrical joints. We utilize the dialytic elimination method to simplifythe synthesis equations and to obtain a univariate ninth degree polynomial equation.Among the nine sets of solutions, two of them are infinite, and one is the displacementscrew from the first position to the second position. Therefore, we have atmost six real solutions that can be used to design spatial sliders for the four-positionsynthesis problem. A numerical example is provided in to demonstrate the validityof the solution procedure.
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