Inverse and Forward Kinematic Analysis of a 6-DOF Parallel Manipulator Utilizing a Circular Guide

Abstract

The proposed study focuses on the inverse and forward kinematic analysis of a novel 6-DOF parallel manipulator with a circular guide. In comparison with the known schemes of such manipulators, the structure of the proposed one excludes the collision of carriages when they move along the circular guide. This is achieved by using cranks (links that provide an unlimited rotational angle) in the manipulator kinematic chains. In this case, all drives stay fixed on the base. The kinematic analysis provides analytical relationships between the end-effector coordinates and six controlled movements in drives (driven coordinates). Examples demonstrate the implementation of the suggested algorithms. For the inverse kinematics, the solution is found given the position and orientation of the end-effector. For the forward kinematics, various assembly modes of the manipulator are obtained for the same given values of the driven coordinates. The study also discusses how to choose the links lengths to maximize the rotational capabilities of the end-effector and provides a calculation of such capabilities for the chosen manipulator design.

Workspace and performance analysis of a 6-DOF hexapod-type manipulator with a circular guide

“…As said earlier, angle normalδ i is limited by design to prevent collisions between the adjacent carriages. Assuming the planar section of the mechanism is symmetric, we can write 17 where normalδ m a x is a maximum allowable value of angle normalδ i ; normalΔ is a distance between adjacent carriages in their most close position; normalγ is an angular width of the carriage.…”

“…To find vectors bolds ^ i and boldp A i , used in equations (11) and (12), we apply the inverse kinematics algorithm. 17,18 Geometrically, we should find points where a sphere, centered in B i with radius L , intersects a circular guide. We know this intersection will occur because we check points from { boldp P } that already satisfy constraints 1–3.…”

An Approach to Determine All Joint Motions of Parallel Robot and Its Software Development

“…Then other variables would be derived by introducing the other geometric conditions. In spite of a little computation cost, observation and experience are required to find out the special geometric condition [26], leading to case-by-case study and not convenient for the programming of software development. The algebraic method based on homogeneous transformation matrix, Lie groups, dual quaternions provide a more general and systematic process for the inverse kinematics of parallel robots [27].…”

Nonprehensile Manipulation of Parts on a Horizontal Circularly Oscillating Platform with Dynamic Dry Friction Control

“…Parts on a horizontal platform can be moved by various means. For example, this can be performed by using parallel manipulators [ 1 , 2 , 3 , 4 ] by applying piezoelectric or electromagnetic actuated planar micromanipulators [ 5 , 6 , 7 , 8 ], by pushing with robot end-effectors [ 9 , 10 , 11 ], by transporting with devices which move together with the parts to be displaced (e.g., mobile robots) [ 12 , 13 , 14 ], by employing actuator arrays under a flexible surface [ 15 ], by applying acoustic manipulation techniques [ 16 , 17 , 18 , 19 ], etc.…”