A raíz de holguras, usamos la mordaza de carpintero.

Yes. A raíz de is a common fixed expression meaning because of, as a result of, or following.

In this sentence, it introduces the cause:

• A raíz de holguras = because of looseness / due to gaps or play

It is often used in slightly formal or neutral Spanish, and very often when one thing happens as a consequence of another.

Compare:

• A raíz de un problema, cambiamos el diseño. = As a result of a problem, we changed the design.
• A raíz del accidente, tomó más precauciones. = Following the accident, he took more precautions.

It can sound a bit more formal than just por.

Here, holguras is a technical or semi-technical word. It usually refers to slack, play, clearance, looseness, or gaps/tolerance in how parts fit together.

So it does not usually mean emotional or general freedom here. In mechanical, carpentry, or construction contexts, holgura often refers to a part not fitting tightly enough.

Examples:

• Hay holgura en la unión. = There is play/slack in the joint.
• Estas piezas tienen demasiada holgura. = These parts have too much clearance/slack.

So in your sentence, holguras suggests that something is loose enough that a clamp or vise is needed.

The plural suggests there are multiple loose points, several gaps, or more than one instance of slack/play.

Spanish often uses the plural for this kind of technical idea when the looseness appears in different places or in a general repeated way.

Compare:

• Hay holgura. = There is slack/play.
• Hay holguras. = There are several loose spots / multiple clearances / repeated looseness issues.

So the plural makes sense if the speaker is referring to more than one gap or fitting issue.

Both are possible, but they do not feel exactly the same.

• A raíz de holguras sounds more general or indefinite: because of looseness / because of some slack.
• A raíz de las holguras would sound more specific: because of the particular gaps/looseness already mentioned or known from the context.

Spanish often omits the article when speaking in a broad or non-specific way, especially with abstract or technical nouns.

So:

• A raíz de holguras = due to looseness/slack in general
• A raíz de las holguras = due to those specific gaps/slack we are talking about

Usamos is the present indicative. In a sentence like this, it usually means one of these:

1. A habitual action

   • Because of looseness, we use the clamp.

2. A general procedure

   • When there is slack, we use the carpenter’s clamp.

3. A present description of what we do

   • We use the clamp because of the looseness.

Other tenses would change the meaning:

• Usábamos = we used to use / we were using
• Hemos usado = we have used
• Usemos = let’s use / that we use (subjunctive)

So usamos is the normal choice if the speaker is stating a fact or routine.

Using la suggests that the tool is specific, known, or the standard one in that context.

So:

• Usamos la mordaza de carpintero = We use the carpenter’s clamp/vise
  This may mean the listener already knows which one, or that it is the usual tool for the job.

If you said:

• Usamos una mordaza de carpintero

that would sound more like:

• We use a carpenter’s clamp
• one example of that kind of tool, not necessarily a specific known one

Spanish uses the definite article quite often where English might be a little freer.

Not necessarily. Here, de carpintero most likely describes the type or use of the tool, not ownership.

So mordaza de carpintero means something like:

• carpenter’s clamp
• woodworking clamp
• clamp used in carpentry

This use of de + noun is very common in Spanish to classify things.

Examples:

• mesa de comedor = dining table
• cepillo de dientes = toothbrush
• gafas de sol = sunglasses

So de carpintero here means for carpentry / used by carpenters / associated with carpentry, not necessarily owned by a carpenter.

It is understandable, but depending on the exact tool, speakers in Spain might more often say:

• sargento
• gato
• gato de apriete
• tornillo de banco if it is a bench vise rather than a clamp

Mordaza can refer to a clamping device or jaws, but in everyday workshop language in Spain, the most natural word may vary by region and by the exact tool.

So the sentence is understandable, but if you are aiming for very natural Spain Spanish, it may be worth checking which specific tool is meant:

• a clamp
• a vise
• jaws
• a bench-mounted holding tool

Yes, that alternative is also grammatically correct.

The original:

• A raíz de holguras, usamos la mordaza de carpintero.

puts the cause first, which gives it emphasis. It sounds a bit like:

• Because of looseness, we use the carpenter’s clamp.

The other order:

• Usamos la mordaza de carpintero a raíz de holguras.

puts the main action first:

• We use the carpenter’s clamp because of looseness.

Both are possible. The first one sounds slightly more marked or explanatory because it foregrounds the reason.

They can all express cause, but they do not feel exactly the same.

• por = the most general and common way to say because of
• debido a = more formal, often used in careful or written language
• a causa de = clearly causal, sometimes with a negative tone
• a raíz de = as a result of / following / stemming from, often focusing on consequence

Examples:

• Por holguras, usamos la mordaza. = Because of looseness, we use the clamp.
• Debido a holguras, usamos la mordaza. = Due to looseness, we use the clamp.
• A causa de holguras, usamos la mordaza. = Because of looseness, we use the clamp.
• A raíz de holguras, usamos la mordaza. = As a result of looseness, we use the clamp.

In many contexts, they overlap, but a raíz de often sounds a bit more like one thing has led to another.

It sounds fairly technical or specialized, mainly because of:

• holguras
• mordaza de carpintero

A native speaker would understand it, especially in a workshop, engineering, DIY, or carpentry context. But outside those contexts, it may sound less everyday than something like:

• Como hay juego, usamos un sargento.
• Por la holgura, usamos una mordaza.

So the sentence is not wrong, but it belongs more to practical/technical language than to casual everyday conversation.