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It is the intent of this manuscript to provide a general treatment of braiding: past, present, and future. A history and evolution of braiding, braiding machinery, and related engineering developments is provided with emphasis on the design, manufacture, and analysis of braided fabrics and composites. Some recent developments are briefly described, including: 1. a composite braider with axial yarns which interlace with the helicals, and in which the helical yarns do not interlace with each other-a machine now under commercial development, 2. a new braided structure, called the true triaxial braid, produced by the new machine or by proper carrier loading on a conventional Maypole braider; and 3. a computer controlled take-up system using image analysis to monitor and control braid formation. Original work ongoing at Auburn University is described and involves Jacquard lace braids with open structures for use in composites, computer aided design (CAD), computer aided manufacturing (CAM), and analysis of ordinary and lace braids for composite applications. This paper is an expanded version of an invited presentation under the title "New Directions in Braiding" at a Fiber Society presentation in Bursa, Turkey, in the spring of 2010 [1]. Historical Context Braiding has been an important process throughout history of transforming fibers to more useful forms. It is arguably the first textile process, practiced by ancient civilizations [3]. Smaller, natural-fiber strands were braided in order to produce larger, stronger structures such as rope. Several online encyclopedias and other sources place the origins of braided rope at more than 17,000 years ago [4]. Ancient Chinese and Japanese documents record that braiding was in use before 4,000 BC [5-6]. Braiding in the context of ancient history is simply considered the oblique interlacing of three or more strands [6-7]. The original braiding machine predates the Industrial Revolution [8]. As mankind became more sophisticated, so did the methods of producing textiles, including braids. A modern definition of braiding is given by the German Industrial Standard DIN 60000 as "two or three-dimensional fabrics with even thread density

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The final structure of a braid is a consequence of force interactions among yarns in the convergent zone. In Part 1, the influence of friction forces on the final braided structure was discussed via kinematic analysis. A transformation from a 3-D cone to a 2-D plane was made for the mechanics analysis. A mechanics model is proposed in this paper to determine the braid angle by considering interlacing forces. Equilibrium equations for the braiding process are deduced. A Newton-Raphson method is used to solve the nonlinear algebraic equation set. Experiments have been conducted to produce braids at different machine speeds and with different tensions, and reveal that the mechanics model is potentially a better predictor of final braid structure than the kinematic analysis.

Circular braiding is a manufacturing process for making circular braided fabrics. Relative sliding of yarns during their interlacing motion introduces friction which limits the density of the braided fabric. A kinematic analysis is presented in this paper. Yarns’ absolute motion, relative sliding motion and twist motion in the convergent zone are found to be important quantities in braid kinematics that impact the final braid structure. The straight yarn assumption, which ignores the effect of interyarn forces, is analyzed in detail for its validity in calculating the braid angle. In Part 2 of this paper series a mechanics model is proposed to determine the braid angle by considering interlacing forces and their effects on the braided structure.