Manipulator Configurations Based on Rotary-Linear (R-L) Actuators and Their Direct and Inverse Kinematics

1988 ◽  
Vol 110 (4) ◽  
pp. 397-404 ◽  
Author(s):  
D. Kohli ◽  
Soo-Hun Lee ◽  
Kao-Yueh Tsai ◽  
G. N. Sandor
Keyword(s):  
Inverse Kinematics ◽  
Polynomial Equation ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Serial Link ◽  
New Type ◽  
Computationally Intensive ◽  
Six Degree Of Freedom ◽  
Two Degree Of Freedom ◽  
Direct Kinematics

In this paper, a new type of two-degree-of-freedom actuator called the rotary-linear (R-L) actuator is described. The R-L actuator permits a rotation and a translation along the axis of rotation, thus simulating a cylinder pair. The R-L actuators are then used in type synthesis of mechanical manipulator chains. Closed-loop three-, four, five, and six-degree-of-freedom chains containing four to nine links, R-L actuators, revolute pairs (R), prismatic pairs (P), cylindrical pairs (C), and spheric pairs (S) are then obtained. A class of manipulator configurations where the hand is connected to the ground via six-degree-of-freedom dyads or triads and containing three grounded R-L actuators is treated for inverse kinematics. Since all the actuators are on the ground in this configuration, higher payload capacities and smaller actuator sizes can be expected from these configurations. In addition, generally, the computations required for inverse kinematics are also significantly less than those required for serial link open-loop manipulators. The direct kinematics, however, is much more involved and computationally intensive for these manipulators than for serial-link manipulators. The direct kinematics of an example manipulator is derived and requires solution of a 16th-order polynomial equation. Numerical examples are presented for illustration.

scholarly journals Kinematic analysis of the 3-RPS-3-SPR series–parallel manipulator

Robotica ◽  
2018 ◽  
Vol 37 (7) ◽  
pp. 1240-1266 ◽  
Author(s):  
Abhilash Nayak ◽  
Stéphane Caro ◽  
Philippe Wenger
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
End Effector ◽  
Inverse Kinematics Problem ◽  
Univariate Polynomial ◽  
Six Degree Of Freedom ◽  
Independent Parameters ◽  
Direct Kinematics

SUMMARYThis paper deals with the kinematic analysis and enumeration of singularities of the six degree-of-freedom 3-RPS-3-SPR series–parallel manipulator (S–PM). The characteristic tetrahedron of the S–PM is established, whose degeneracy is bijectively mapped to the serial singularities of the S–PM. Study parametrization is used to determine six independent parameters that characterize the S–PM and the direct kinematics problem is solved by mapping the transformation matrix between the base and the end-effector to a point in ℙ7. The inverse kinematics problem of the 3-RPS-3-SPR S–PM amounts to find the location of three points on three lines. This problem leads to a minimal octic univariate polynomial with four quadratic factors.

Kinematics of a New High-Precision Three-Degree-of-Freedom Parallel Manipulator

2006 ◽  
Vol 129 (3) ◽  
pp. 320-325 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three-degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three-DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base mounted, higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of the tangent of the half-angle between one of the limbs and the base plane. Hence, there are at most 16 assembly configurations for the manipulator. In addition, it is shown that the 16 solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

New Type of Two Degree of Freedom Motor Three-Dimensional Tooth Layer Field Application and Solution

2013 ◽  
Vol 391 ◽  
pp. 232-236
Author(s):  
Wen Huan Yang ◽  
Hai Xu Chen ◽  
Shuang Xie ◽  
Chun Ren Fang
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Field Application ◽  
Degree Of Freedom ◽  
Refined Method ◽  
New Type ◽  
Type Motor ◽  
Quasi Newton ◽  
Two Degree Of Freedom ◽  
Non Linear Equations

A new Multi-degree of freedom motor and its establishing of teeth layer parameters have been introduced in the paper, also including application method of database, namely using Quasi-Newton methods to solve the non-linear equations of the new motors magnetic circuit net, formed a refined method for designing and analyzing of motor. The establishment of 3d tooth layer parameters database, is provided for the calculation in the design of the new type motor conveniently.

Design of a 2 DOF Shape Memory Alloy Actuator Using SMA Springs

2021 ◽  
Author(s):  
Hussein F. M. Ali ◽  
Youngshik Kim
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Open Loop ◽  
Degree Of Freedom ◽  
Biologically Inspired ◽  
Loop Control ◽  
Actuator System ◽  
Sma Actuator ◽  
Sma Spring ◽  
Two Degree Of Freedom

Abstract In this paper, we developed two degree of freedom shape memory alloy (SMA) actuator using SMA springs. This module can be applied easily to various applications: device holder, artificial finger, grippes, fish robot, and many other biologically inspired applications, where small size and small wight of the actuator are very critical. This actuator is composed of two sets of SMA springs: one set is for the rotation around the X axis (roll angle) and the other set is for the rotation around the Y axis (pitch angle). Each set contains two elements: one SMA spring and one antagonistic SMA spring. We used an inertia sensor (IMU) and two potentiometers for angles feedback. The SMA actuator system is modeled mathematically and then tested experimentally in open-loop and closed-loop control. We designed and experimentally tuned a proportional integrator derivative (PID) controller to follow the set points and to track the desired trajectories. The main goal of the presented controller is to control roll and pitch angles simultaneously in order to satisfy set points and trajectories within the work space. The experimental results show that the two degree of freedom SMA actuator system follows the desired setpoints with acceptable rise time and overshoot.

Kinematics of a New High Precision Three Degree-of-Freedom Parallel Manipulator

2005 ◽  
Author(s):  
Farhad Tahmasebi
Keyword(s):  
Power Dissipation ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degree Of Freedom ◽  
Base Plane ◽  
Degree Polynomial ◽  
Payload Capacity ◽  
Half Angle ◽  
Three Degree Of Freedom ◽  
Direct Kinematics

Closed-form direct and inverse kinematics of a new three degree-of-freedom (DOF) parallel manipulator with inextensible limbs and base-mounted actuators are presented. The manipulator has higher resolution and precision than the existing three DOF mechanisms with extensible limbs. Since all of the manipulator actuators are base-mounted; higher payload capacity, smaller actuator sizes, and lower power dissipation can be obtained. The manipulator is suitable for alignment applications where only tip, tilt, and piston motions are significant. The direct kinematics of the manipulator is reduced to solving an eighth-degree polynomial in the square of tangent of half-angle between one of the limbs and the base plane. Hence, there are at most sixteen assembly configurations for the manipulator. In addition, it is shown that the sixteen solutions are eight pairs of reflected configurations with respect to the base plane. Numerical examples for the direct and inverse kinematics of the manipulator are also presented.

Research of Nanometer Positioning Stage With Six Degree of Freedom Based on Binary Actuation Principle

2007 ◽  
Author(s):  
Shufeng Sun
Keyword(s):  
Feedback Control ◽  
Theoretical Calculation ◽  
Degree Of Freedom ◽  
Element Analysis ◽  
Positioning Stage ◽  
In Series ◽  
Ultra Precision ◽  
New Type ◽  
Six Degree Of Freedom ◽  
Development Tendency

To adapt the miniaturized development tendency of nanometer positioning devices, a new type of micro-displacement stage with six degree of freedom, which can implement nanometer-level ultra-precision positioning without feedback control is designed. It takes a group of piezoelectric ceramics actuators (PZTAs) connected in series as actuation unit, takes flexure hinges as elastic guide rail. To overcome the non-linearity and hysteresis of PZTAs, binary actuation principle is adopted to control a group of actuators that work together to output many discrete, repeatable displacements. If these displacements are distributed within a scope of several microns, only simple on and off actuator commands may obtain nanometer-level repeatable positioning without feedback control. Theoretical calculation and finite element analysis (FEA) are used to design and simulate the stage. Expressions of rigidity and stress are obtained by theoretical calculation. FEA and experimental results verify the rationality and feasibility of the stage.

Solving the Kinematics of the Most General Six- and Five-Degree-of-Freedom Manipulators by Continuation Methods

1985 ◽  
Vol 107 (2) ◽  
pp. 189-200 ◽  
Author(s):  
L.-W. Tsai ◽  
A. P. Morgan
Keyword(s):  
Polynomial Equation ◽  
Partial Solution ◽  
Degree Of Freedom ◽  
Continuation Methods ◽  
Hand Position ◽  
Closed Form Solutions ◽  
Special Cases ◽  
Prismatic Joints ◽  
Six Degree Of Freedom ◽  
Second Degree

This paper presents a unique approach to the kinematic analysis of the most general six-degree-of-freedom, six-revolute-joint manipulators. Previously, the problem of computing all possible configurations of a manipulator corresponding to a given hand position was approached by reducing the problem to that of solving a high degree polynomial equation in one variable. In this paper it is shown that the problem can be reduced to that of solving a system of eight second-degree equations in eight unknowns. It is further demonstrated that this second-degree system can be routinely solved using a continuation algorithm. To complete the general analysis, a second numerical method—a continuation heuristic—is shown to generate partial solution sets quickly. Finally, in some special cases, closed form solutions were obtained for some commonly used industrial manipulators. The results can be applied to the analysis of both six and five-degree-of-freedom manipulators composed of mixed revolute and prismatic joints. The numerical stability of continuation on small second-degree systems opens the way for routine use in offline robot programming applications.

Degenerate “Star” Bifurcations in a Twinkling Oscillator

2013 ◽  
Vol 136 (2) ◽  
Author(s):  
Smruti R. Panigrahi ◽  
Brian F. Feeny ◽  
Alejandro R. Diaz
Keyword(s):  
Normal Form ◽  
Multiple Equilibria ◽  
Degree Of Freedom ◽  
Negative Stiffness ◽  
Nonlinear Spring ◽  
Mass Chain ◽  
New Type ◽  
Two Degree Of Freedom

We have studied a nonlinear spring-mass chain loaded by a quasistatic pull. The spring forces are assumed to be cubic with intervals of negative stiffness. Depending on the parameters, the system has multiple equilibria. The normal form and the bifurcation behaviors for the single- and two-degree-of-freedom systems are studied in detail. A new type of bifurcation, which we refer to as a star bifurcation, has been observed for the symmetric two-degree-of-freedom system. This bifurcation is of codimension-four for the undamped case and codimension-three or two for the damped case, depending on the form of the damping.

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