can you provide visual examples of these, I learn better when I see examples...
Imagine an agglutinating CVC-syllable language with (1) rules on which consonants can form clusters at syllable boundaries (eg stops and liquids can cluster, but stops and stops can't), and (2) where stress is fixed on the final syllable.
In a word like
tarok, the
o would be stressed. If a suffix (eg plural, or a verb tense) was added, forming
tarokim, the
o would no longer be stressed as it is no longer final - the
i, now final, is stressed.
If unstressed vowels were to delete at some point in the future of this language, that would leave
trok and
tarkim. Note how the three consonants
t r k appear in different positions - a cluster of
tr and a single
k in one form, and a single
t and a cluster of
rk in the other. The changing stress patterns change which vowels delete, and thus which of the three consonants appear as clusters and which have vowels between them.
This is the basic origin of the 3 consonant system - because different vowels can delete from between them, it's only the consonants that remain constant between all forms (and at that, not even their placement stays constant) -
trok and
tarkim have no segments in common except the three consonants. This could be represented as
CCoC and
CaCCim
Now imagine what would happen to a word
takok - it would be suffixed to become
takokim. But now when the unstressed vowels delete, you would get the illegal cluster
*tk:
takok 
*tkok. The vowel wouldn't delete, and so you'd have the pair
takok and
takkim - ie
CaCoC and
CaCCim.
So the same morphological form (a suffixed
-im) gives rise to two different patterns:
CCoC and
CaCCim
CaCoC and
CaCCim
Alternately, the vowel could delete, and an epenthetic vowel (maybe echoing the main vowel) would be added before the cluster:
otkok - there are different strategies possible to deal with such illegal clusters.
As well as simple deletion, affix vowels can cause vowels in the stem to change quality - eg the
i in the suffix could cause the previous vowel in the stem to raise or front:
tarok+
-im tarokim tarkim (clusters block the vowel change)
takok+
-im takokim takkim tekkim (geminate consonants don't block the vowel change)
This leaves you with
CCoC ~ CaCCim and
CaCoC ~ CeCCim as two different pairs of surface forms for the same morphological category (eg singular ~ plural pairs), based solely on which consonants are present. If the second two consonants were unable to form a legal cluster some other repair strategy would be required, leading to another surface form.
What you need to make it work is a system of affixes that cause both the stressed syllable to change, and vowel qualities in the stem to change (ablaut). Then you need deletion of as many unstressed vowels as possible, and rules to cope with all the possible consonant clusters that could arise as a result - that could be vowels not deleted to avoid the cluster forming (in which case the deletion could be shifted to a neighbouring vowel), or one or both of the consonants could assimilate in some way to form a legal cluster (eg
-n+p- -mp- or
-mb-.) If you plan how this happened in the parent language, you'll get a much more detailed, richer and realistic system.
Richness in the triconsonantal daughter language can come from richness in affixes in the parent (different affixes for different genders of nouns or classes of verbs etc) and phonotactics - which clusters are allowed and how the language repairs illegal ones.
Hope this helps.
