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We analyze the parsec-scale jet kinematics from 2007 June to 2018 December ofa sample of $\gamma$-ray bright blazars monitored roughly monthly with the VeryLong Baseline Array at 43 GHz under the VLBA-BU-BLAZAR program. We implement anovel piece-wise linear fitting method to derive the kinematics of 521 distinctemission knots from a total of 3705 total intensity images in 22 quasars, 13 BLLacertae objects, and 3 radio galaxies. Apparent speeds of these componentsrange from $0.01c$ to $78c$, and 18.6\% of knots (other than the "core") arequasi-stationary. One-fifth of moving knots exhibit non-ballistic motion, withacceleration along the jet within 5 pc of the core (projected) and decelerationfarther out. These accelerations occur mainly at locations coincident withquasi-stationary features. We calculate the physical parameters of 273 knotswith statistically significant motion, including their Doppler factors, Lorentzfactors, and viewing angles. We determine the typical values of theseparameters for each jet and the average for each subclass of active galacticnuclei. We investigate the variability of the position angle of each jet overthe ten years of monitoring. The fluctuations in position of thequasi-stationary components in radio galaxies tend to be parallel to the jet,while no directional preference is seen in the components of quasars and BLLacertae objects. We find a connection between $\gamma$-ray states of blazarsand their parsec-scale jet properties, with blazars with brighter 43 GHz corestypically reaching higher $\gamma$-ray maxima during flares.

Kinematics of Parsec-Scale Jets of Gamma-Ray Bright Blazars at 43 GHz during Ten Years of the VLBA-BU-BLAZAR Program