KINEMATIC SYNTHESIS AND ANALYSIS OF THE RACK AND PINION MULTIPURPOSE MECHANISM

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rock occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included

Kinematic Synthesis and Analysis of the Rack and Pinion Multi-Purpose Mechanism

The general procedure for synthesizing the rack and pinion mechanism up to seven precision conditions is developed. To illustrate the method, the mechanism has been synthesized in closed form for three precision conditions of path generation, two positions of function generation, and a velocity condition at one of the precision points. This mechanism has a number of advantages over conventional four bar mechanisms. First, since the rack is always tangent to the pinion, the transmission angle is always 90 deg minus the pressure angle of the rack. Second, with both translation and rotation of the rack occurring, multiple outputs are available. Other advantages include the generation of monotonic functions for a wide variety of motion and nonmonotonic functions for a full range of motion as well as nonlinear amplified motions. In this work the mechanism is made to satisfy a number of practical design requirements such as completely rotatable input crank and others. By including the velocity specification, the designer has considerably more control of the output motion. The method of solution developed in this work uses the complex number method of mechanism synthesis. A numerical example is included.

RACK: RApid Clustering using K-means algorithm

The k-means algorithm is an extremely popular technique for clustering data. One of the major limitations of the k-means is that the time to cluster a given dataset D is linear in the number of clusters, k. In this paper, we employ height balanced trees to address this issue. Specifically, we make two major contributions, (a) we propose an algorithm, RACK (acronym for RApid Clustering using k-means), which takes time favorably comparable with the fastest known existing techniques, and (b) we prove an expected bound on the quality of clustering achieved using RACK. Our experimental results on large datasets strongly suggest that RACK is competitive with the k-means algorithm in terms of quality of clustering, while taking significantly less time.

Rack Level Modeling of Air Flow Through Perforated Tile in a Data Center

Effective air flow distribution through perforated tiles is required to efficiently cool servers in a raised floor data center. We present detailed computational fluid dynamics (CFD) modeling of air flow through a perforated tile and its entrance to the adjacent server rack. The realistic geometrical details of the perforated tile, as well as of the rack are included in the model. Generally, models for air flow through perforated tiles specify a step pressure loss across the tile surface, or porous jump model based on the tile porosity. An improvement to this includes a momentum source specification above the tile to simulate the acceleration of the air flow through the pores, or body force model. In both of these models, geometrical details of tile such as pore locations and shapes are not included. More details increase the grid size as well as the computational time. However, the grid refinement can be controlled to achieve balance between the accuracy and computational time. We compared the results from CFD using geometrical resolution with the porous jump and body force model solution as well as with the measured flow field using particle image velocimetry (PIV) experiments. We observe that including tile geometrical details gives better results as compared to elimination of tile geometrical details and specifying physical models across and above the tile surface. A modification to the body force model is also suggested and improved results were achieved.