To improve high motion accuracy and efficiency in the high-speed operation of a 4-DOF (4 degrees of freedom) redundant parallel robot. this paper introduces a trajectory planning of the parallel robot in joint space based on the twelve-phase sine jerk motion profile. The 12-phase sine jerk motion profile utilizes the characteristics of a sine function. Furthermore. https://countryscenesaddleryandpetsuppliers.shop/product-category/western-headstall/