Tension vector and structure matrix associated force sensitivity of a 6-DOF cable-driven parallel robot

Abstract

This paper investigates the force sensitivity of 6-DOF cable-driven parallel robots (CDPRs) in order to propose a better force measurement device. Kinematics and dynamics for a CDPR of n-DOF are deduced and formulated, and algorithms for calculating the cable tension are developed. Then, by defining geometrical parameters related to the dimensions and configurations of the CDPRs, optimal methods for determining force sensitivity with respect to the structure matrix and twist vector of the 6-DOF CDPRs with two different moving platforms (i.e. a cubic-shaped, and a flat moving platform) are proposed. By using numerical examples integrated with external twists obtained from wind tunnel tests, simulations and analysis for the two type of 6-DOF CDPRs are carried out. The simulation results help identify the optimal dimensions that can be used to design 6-DOF-CDPR-based force measuring devices with high force sensitivity. Experiment validation is also conducted to verify the method proposed in this paper.

Kinematics and dynamics analysis of a six-degree of freedom parallel manipulator

“…As with complex joints, they can be replaced by some basic joints, so the kinematic sketch of the first kinematic chain can be described as Figure 5. S 1 1 is the axis of the prismatic joint, spherical joint B 1 is substituted by three revolute joints, and S 1 2 , S 1 3 , S 1 4 are their axes. In a similar way, universal joint U 1 is equivalent to two intersecting revolute joints S 1 5 , S 1 6 .…”

“…In a similar way, universal joint U 1 is equivalent to two intersecting revolute joints S 1 5 , S 1 6 . Assuming that S 1 1 and S 1 2 are parallel to X b , S 1 4 pointing to the length direction of the strut B 1 U 1 , S 1 6 is parallel to U 1 O 0 . In what follows, S 1 3 perpendicular to S 1 2 and S 1 4 , and S 1 5 is normal to S 1 4 and S 1 6 .…”

“…Assuming that S 1 1 and S 1 2 are parallel to X b , S 1 4 pointing to the length direction of the strut B 1 U 1 , S 1 6 is parallel to U 1 O 0 . In what follows, S 1 3 perpendicular to S 1 2 and S 1 4 , and S 1 5 is normal to S 1 4 and S 1 6 . What is more, all of these vectors are unit vectors which can be described as follows…”

“…Take the first kinematic chain described in Figure 4 as an example, T 1 4 denotes the transformation matrix from the local coordinate system O 1 -X 1 Y 1 Z 1 to the global coordinate system. X 1 -axis is parallel to S 1 4 , Z 1 -axis is parallel to S 1 3 , and i, k, j are the unit vectors along axes X 1 , Y 1 , Z 1 , respectively, then T 1 4 can be addressed from following equation…”

“…In practice, an aircraft model will move along the given trajectory, which usually contains pitch, roll, yaw, heave, surge, and sway motion about the reference coordinate system, so a kind of 6-DOF mechanisms with high precision and stabilization are required to achieve the demands of corresponding tests. 1,2 Parallel manipulators are closed-loop mechanical structures composed of a moving platform coupled to a fixed base by serial limbs, which usually can provide multi-degree of freedom with great comprehensive performance, 3,4 and they will be a good choice for wind tunnel tests.…”