Reconfiguration Analysis of a Variable Degrees-of-Freedom Parallel Manipulator With Both 3-DOF Planar and 4-DOF 3T1R Operation Modes

Reconfiguration analysis is essential for the design and control of multi-operation-mode parallel manipulators (PMs). This paper deals with the reconfiguration analysis of a variable-DOF (degrees-of-freedom) multi-operation-mode E/PPPR = PM, i.e. a PM with both 3-DOF planar operation mode and 4-DOF 3T1R (or Schönflies motion which has three translational DOF and 1 rotational DOF) operation mode. The axes of rotation of the moving platform in the 3-DOF planar operation mode are not parallel to the axes of rotation of the moving platform in the 4-DOF 3T1R operation mode. In the reconfiguration analysis, the orientation of the moving platform is represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion). The reconfiguration analysis shows that the E/PPPR = PM has two 4-DOF 3T1R operation modes and two 3-DOF planar operation modes, including the two expected operation modes. The transition configurations between each pair of operation modes are also identified.

Reconfiguration Analysis of a Two Degrees-of-Freedom 3-4R Parallel Manipulator With Planar Base and Platform1

This paper deals with a 2-DOF (degrees-of-freedom) 3-4R parallel manipulator (PM) with planar base and platform—a novel PM with multiple operation modes (or disassembly free reconfigurable PM) that can use the minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM are derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler–Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace-based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R PM with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

Reconfiguration Analysis of a 2-DOF 3-4R Parallel Manipulator With Planar Base and Platform

This paper deals with a 2-DOF 3-4R parallel manipulator (PM) with planar base and platform — a novel PM with multiple operation mode (or disassembly-free reconfigurable PM) with minimum number of actuated joints. At first, a set of constraint equations of the 3-4R PM is derived with the orientation of the moving platform represented using a Euler parameter quaternion (also Euler-Rodrigues quaternion) and then solved using the algebraic geometry method. It is found that this 3-4R PM has six 2-DOF operation modes, including the two expected spherical translation mode and sphere-on-sphere rolling mode when the PM was synthesized. The motion characteristics of the moving platform are obtained using the kinematic interpretation of Euler parameter quaternions with certain number of constant zero components, which was presented in a recent paper by the first author of this paper, instead of the eigenspace based approach in the literature. The transition configurations, which are constraint singular configurations, among different operation modes are also presented. This work provides a solid foundation to the development and control of the 2-DOF 3-4R parallel manipulator (PM) with both 2-DOF spherical translation mode and 2-DOF sphere-on-sphere rolling mode.

Efficiency of Methods for Kinematic Analysis Using the Algebra of Rotations

The algebra of rotations is an alternative method for describing rigid body rotations. It can be efficiently used in the kinematic analysis of robots. One of the basic problems of the algebra of rotations is to determine the resultant sum of a number of sequential joint rotations. For this calculation, four new methods, in addition to the two methods already available in the literature, are proposed in this paper. The six methods are then compared analytically and numerically on the basis of the computational efficiency. The limitations to each of the methods are also discussed. It is found that the equivalent Rodrigues parameter method is the most efficient. However, the equivalent Euler parameter method is the preferred method for use since it is infinity free, initial vector independent and reasonably efficient.