We study fluidic assembly and packing of spherical particles in rectilinear microchannels that are terminated by a flow constriction. First, we introduce a method for active assembly of particles in the confined microchannels by triggering a local constriction in the fluid channel using a partially closed membrane valve. This microfluidic valve allows active, on-demand particle assembly as opposed to previous passive assembly methods based on terminal channels and weirs. Second, we study the three-dimensional assembly and packing of particles against a weir in confined rectilinear microchannels. The packings result in achiral particle chains with alternating (zigzag) structure. This structure is characterized by a single, repeated bond angle whose components projected into the frame of the channel are quantified by confocal microscopy and image processing. Brownian dynamics simulation of the packing comprehensively delineates the range of bond angles possible in narrow, rectilinear microchannels as well as the complex dependence of these angles on the relative dimensions of the channel and particles. The simulations of the three-dimensional packings are accurately modeled by a compact theory based on trigonometric relationships. The experimentally measured bond angles show excellent agreement with the simulations, thereby validating the functional dependence of the achiral packing bond angles on channel dimensions. This functional relationship is immediately useful for the design of anisotropic particles by microfluidic synthesis.