Synthesis of mechanisms with spherical helix curve based on an algebraic method

In this study, we take the spherical helix curve as the given trajectory and use algebraic methods to derive the motion polynomial of the spherical helix curve. By decomposing the motion polynomial, we obtain a serial chain with the spherical helix curve as the end trajectory, these serial chains are then combined to form a new single-loop mechanism. To better demonstrate the end trajectory of the single-loop mechanism, a novel 7R (revolute) single-loop mechanism is chosen to compute the forward solution. The calculation shows that the 7R mechanism has one degree of freedom, and its end trajectory is confirmed to be a spherical helix curve. A novel gripper is then created by using the 7R mechanism as a unit and following a specific networking method.