Forward Kinematic Model Resolution of a Special Spherical Parallel Manipulator: Comparison and Real-Time Validation

Abstract

This paper deals with a special architecture of Spherical Parallel Manipulators (SPMs) designed to be a haptic device for a medical tele-operation system. This architecture is obtained by replacing the kinematic of one leg of a classical 3-RRR SPM (R for revolute joint). The Forward Kinematic Model (FKM) is particularly addressed to allow the new master device to control the motion of a slave surgical robot. For this purpose, three methods are presented to solve the FKM and compared based on the criterion of time consuming and accuracy. For each method, namely, classic FKM, Improved method and serial FKM, the resolution procedure is detailed and the experimental validation is presented. After comparison, the serial approach involving the use of three sensors located on one leg of the master device is revealed as the most suitable. Experimental validation of the real-time motion control is successfully performed using the serial FKM.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

“…So far, most studies have focused on the kinematic issues of RSPMs, while quite a few have referred to the dynamic control of these robots. For RSPMs, several studies have been reported on a variety of relevant problems, which include modeling of workspace in joint and Cartesian space [14][15][16][17], inverse and forward kinematic analysis to obtain analytically unique real-time solutions [18][19][20][21][22][23][24][25], design and optimization [26][27][28][29][30][31][32], design and robustness [33], singularity analysis, and derivation of Jacobian matrices [34,35]. However, the constrained kinematic analysis has gone unnoticed in the literature.…”

Configuration design and load capacity analysis of pelvic fracture reduction robot

“…1, which consists of two parts: the 3RRR parallel mechanism and the 3D moving mechanism. 3RRR parallel mechanism is used for the 3D rotational reduction [20]- [22], and the 3D moving mechanism is used for 3D moving reduction. 3RRR parallel mechanism is fixedly connected to the injured pelvis by a pelvic clamping instrument.…”

Topological Analysis of a Novel Compact Omnidirectional Three-Legged Robot with Parallel Hip Structures Regarding Locomotion Capability and Load Distribution

“…In [14,16], a manipulator for precise and high-speed orientation of a camera-the Agile Eye-was built. In [17][18][19] the manipulator was utilized as an device for surgery applications and in [20] in a human hip exoskeleton context. In combination with the knee joint, each leg of the robot is a serial-parallel-manipulator on its own, which is connected by the central torso part.…”

“…As it can be observed in Equations ( 18) and (19), it is possible to decompose the matrices X * and Y * into X * = X D and Y * = Y D with the diagonal matrix…”

“…In this sense, it should be considered to not explicitly calculate the Jacobian matrix J by either Equation ( 26) or (28), as this may be slow and numerically inaccurate in actual controller implementations. Instead, by employing Equations ( 18) and (19) after each other, the system of equations may be solved by Gauß elimination, yielding the required vector, without explicitly calculating the manipulator Jacobian matrix.…”