  An unconventional and innovative mechanical transmission component, the
Curved Groove Ball Bearing without Retainer (CGBBR), is introduced in this
paper to facilitate the conversion between rotary and reciprocating motion. The
CGBBR boasts several advantages over conventional motion conversion mechanisms,
including a streamlined and compact structure, as well as the mitigation of
high-order vibrations. This paper delves into the design methodology,
structural attributes, kinematic principles, and dynamic response properties of
the CGBBR. A novel design method named closed curve envelopment theory is
proposed to generate the distinctive spatial surface structure of the CGBBR.
Moreover, a design scheme is presented that employs the concept of
diameter-stroke ratio for CGBBR implementation. A calculation methodology is
also introduced for determining the number of rolling elements within the
CGBBR, which serves as the foundation for subsequent optimization design. This
paper deeply analyzes the kinematics principle of CGBBR and provides a new
insight of motion conversion in mechanism.
