Spatial Mechanism Kinematics and Synthesis

2013 ◽  
pp. 137-186
Author(s):  
Kevin Russell ◽  
Qiong Shen ◽  
Raj S. Sodhi
Keyword(s):  
Author(s):  
Javier Rolda´n Mckinley ◽  
Carl Crane ◽  
David B. Dooner

This paper introduces a reconfigurable closed-loop spatial mechanism that can be applied to repetitive motion tasks. The concept is to incorporate five pairs of non-circular gears into a six degree-of–freedom closed-loop spatial chain. The gear pairs are designed based on given mechanism parameters and a user defined motion specification of a coupler link of the mechanism. It is shown in the paper that planar gear pairs can be used if the spatial closed-loop chain is comprised of six pairs of parallel joint axes, i.e. the first joint axis is parallel to the second, the third is parallel to the fourth, ..., and the eleventh is parallel to the twelfth. This paper presents the synthesis of the gear pairs that satisfy a specified three-dimensional position and orientation need. Numerical approximations were used in the synthesis the non-circular gear pairs by introducing an auxiliary monotonic parameter associated to each end-effector position to parameterize the motion needs. The findings are supported by a computer animation. No previous known literature incorporates planar non-circular gears to fulfill spatial motion generation needs.


Author(s):  
S-T Chiou ◽  
J-C Tzou

It has been shown in a previous work that a frequency term of the shaking force of spatial mechanisms, whose hodograph is proved to be an ellipse, can be eliminated by a pair of contrarotating counterweights. In this work, it is found that the relevant frequency term of the shaking moment is minimized if the balancing shafts are coaxial at the centre of a family of ellipsoids, called isomomental ellipsoids, with respect to (w.r.t.) any point on an ellipsoid, as is also the root mean square (r.m.s.) of the relevant frequency term of the shaking moment. It can also be minimized even though the location of either shaft, but not both, is chosen arbitrarily on a plane. The location of the second shaft is then determinate. In order to locate the centre, a derivation for the theory of isomomental ellipsoids of a frequency term of the shaking moment of spatial mechanisms is given. It is shown that the r.m.s. of a frequency term shaking moment of a spatial mechanism w.r.t. the concentric centre of the isomomental ellipsoids is the minimum. Examples of a seven-link 7-R spatial linkage and a spatial slider-crank mechanism are included.


2014 ◽  
Vol 84 (19) ◽  
pp. 2065-2073 ◽  
Author(s):  
Recep Eren ◽  
Mesrur Erturk ◽  
Barıs Hascelik

This paper presents an approach for the kinematic design of a rapier drive mechanism containing a spatial mechanism and analyses rapier motion curve. Kinematic design and analysis equations are derived and then the link lengths of the spatial mechanism are calculated in order to satisfy the critical rapier positions inside and outside the shed. In this way, the portions of one loom revolution, during which the rapiers are inside and outside the shed, are determined. The rapier motion curve is obtained by using kinematic analysis equations. It is shown that the position of the oscillating link in the spatial mechanism and the loom main shaft angle at which the rapier enters the shed have the most significant effect on the rapier motion curve. The gear ratio has also some effect on the rapier motion curve. Different rapier motion curves are obtained by changing these parameters and the suitability of these curves for rapier motion is discussed.


1971 ◽  
Vol 93 (1) ◽  
pp. 221-226 ◽  
Author(s):  
A. H. Soni ◽  
P. R. Pamidi

Using (3 × 3) matrices with dual-number elements, closed form displacement relationships are derived for a spatial five-link R-R-C-C-R mechanism. The input-output closed form displacement relationship is an eighth degree polynomial equation. A numerical example is presented.


1971 ◽  
Vol 93 (1) ◽  
pp. 67-73 ◽  
Author(s):  
M. S. C. Yuan ◽  
F. Freudenstein ◽  
L. S. Woo

The basic concepts of screw coordinates described in Part I are applied to the numerical kinematic analysis of spatial mechanisms. The techniques are illustrated with reference to the displacement, velocity, and static-force-and-torque analysis of a general, single-degree-of-freedom spatial mechanism: a seven-link mechanism with screw pairs (H)7. By specialization the associated computer program is capable of analyzing many other single-loop spatial mechanisms. Numerical examples illustrate the results.


Author(s):  
M.G Zaliubovskyi ◽  
I.V Panasiuk ◽  
Yu.I Smirnov ◽  
V.V Malyshev
Keyword(s):  

2018 ◽  
Vol 10 (4) ◽  
Author(s):  
Peter L. Wang ◽  
Ulrich Rhem ◽  
J. Michael McCarthy

This paper applies kinematic synthesis theory to obtain the dimensions of a constrained spatial serial chain for a valve mechanism that cleans and closes a soil conditioning port in a tunnel boring machine. The goal is a smooth movement that rotates a cylindrical array of studs into position and then translates it forward to clean and close the port. The movement of the valve is defined by six positions of the revolute-prismatic-revolute (RPR) serial chain. These six positions are used to compute the dimensions of the two spherical spherical (SS) dyads that constrain the RPR chain to obtain a one degree-of-freedom spatial mechanism. An example design of this valve mechanism is provided in detail.


Author(s):  
A. J. Kakatsios ◽  
S. J. Tricamo

Abstract A novel integrated technique permitting the simultaneous optimization of kinematic and dynamic characteristics in the synthesis of spatial mechanisms is shown. The nonlinear programming formulation determines mechanism variables which simultaneously minimize the maximum values of bearing reactions, joint torques, driving torque, shaking moment, and shaking force while constraining the maximum kinematic structural error to a prescribed bound. The method is applied to the design of a path generating RRSS spatial mechanism with prescribed input link timing. Dynamic reactions in the mechanisms synthesized using the integrated technique were substantially reduced when compared to those of a mechanism synthesized to satisfy only the specified kinematic conditions.


Author(s):  
B. R. Thatch ◽  
A. Myklebust

Abstract Creation of input specifications for synthesis or analysis of spatial mechanisms can be a significant problem. A graphics preprocessor which interactively assists in the definition of spatial mechanism problems is described. New methods of depth cucing and six DOF data entry are presented. To achieve graphics device-independence, the proposed graphics standard PHIGS (Programmer’s Hierarchical Interactive Graphics System) is used. Examples of application are presented including generation of input commands for Integrated Mechanisms Program (IMP) and generation of input for spatial mechanism synthesis routines.


Author(s):  
G. K. Ananthasuresh ◽  
Steven N. Kramer

Abstract The closed form solution of the analysis of the RSCR (Revolute-Spherical-Cylindrical-Revolute) spatial mechanism is presented in this paper. This work is based on the geometric characteristics of the mechanism involving the following three cases: the cone, the cylinder and the one-sheet hyperboloid. These cases derive their names from the nature of the locus of the slider of the linkage as viewed from the output side. Each case is then treated separately to develop a closed form, geometry based analysis technique. These analysis modules are then used to optimally synthesize the mechanism for function, path and motion generation problems satisfying precision conditions within prescribed accuracy limits. The Selective Precision Synthesis technique is employed to formulate the nonlinear inequality constraints. These constraints along with an objective function and other constraints are solved using the Generalized Reduced Gradient method of optimization. In addition, the use of mobility charts is used to aid the designer in making a judicious choice for the initial design point before invoking the optimization method. The determination of the transmission angle for the RSCR mechanism is also described and numerical examples for function, path and motion generation are also included. This new closed form method of analysis based on geometric characteristics is computationally less intensive than other available techniques for spatial mechanism analysis and helps in the visualization of the physical mechanism; something that is not possible with most vector and matrix methods.


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