Multipoint orbital forming machine flares out machined, semipierced, die-cast, or molded studs, pins, tabs, and bosses to secure mating part without rivets, screws, or other fasteners. Blanked ridges, protrusions, and integral projections of malleable material can be formed to anchor components. Multispindle heads can be interchanged or retooled for varying patterns. Nonspinning tools maintain constant line contact with workpiece without intermittent peening motion, noise, or vibration.