The atomic radii of transition metals typically decrease as you move across the periodic table from left to right, primarily due to an increase in nuclear charge.

As you progress across the periodic table, particularly through groups 3 to 12 where transition metals are located, the atomic radii generally contract. This contraction occurs because the nuclear charge increases, which effectively pulls the electrons closer to the nucleus, resulting in a smaller atomic radius. While this trend is observable, it is not as clear-cut as it is for main group elements.

Transition metals possess partially filled $d$ orbitals. When moving from left to right across a period, electrons are added sequentially to these $d$ orbitals, alongside an increase in the number of protons within the nucleus. This added nuclear charge enhances the attractive force on the electrons, which draws them nearer to the nucleus and contributes to a reduction in atomic radius.

However, the decrease in atomic radius among transition metals is less pronounced compared to that observed in main group elements. This can be attributed to the shielding effect experienced by the $d$ electrons. Inner electrons effectively shield the outer electrons from the full force of the nuclear charge, which mitigates the expected decrease in atomic radius.

Moreover, $d$ orbitals are more diffuse than $s$ and $p$ orbitals, extending further from the nucleus. This characteristic also plays a role in lessening the extent of the atomic radius decrease across the transition metals.

It is important to note that there are exceptions to this general trend. For instance, the atomic radii of elements in the second and third transition series do not always exhibit a consistent decrease. This inconsistency is often attributed to the lanthanide contraction, a phenomenon where the $4f$ electrons in lanthanide elements do not shield the increasing nuclear charge as effectively as anticipated, leading to smaller atomic radii.

In conclusion, while the atomic radii of transition metals generally decrease across the periodic table due to the increasing nuclear charge, the trend is complicated by factors such as the shielding effect of inner electrons and the diffuse nature of the $d$ orbitals.